STOCKHOLDER'S AND REGISTRATION RIGHTS AGREEMENT

Exhibit 10.4

STOCKHOLDER’S AND REGISTRATION RIGHTS AGREEMENT

This STOCKHOLDER’S AND REGISTRATION RIGHTS AGREEMENT, dated as of August 31, 2009 (this “ Agreement ”), is by and between CareFusion Corporation, a Delaware corporation (the “ Company ”), and Cardinal Health, Inc., an Ohio corporation (the “ Parent ”).

WHEREAS, pursuant to the Separation Agreement, dated as of July 22, 2009 (the “ Separation Agreement ”), by and between the Company and the Parent, Parent will distribute at least 80% of the outstanding shares of Common Stock (as defined below) to the Parent’s shareholders (the “ Distribution ”);

WHEREAS, if any shares of Common Stock are not distributed in the Distribution (such shares not distributed in the Distribution, the “ Retained Shares ”), then the Parent may dispose of these shares through one or more transactions, including pursuant to one or more transactions registered under the Securities Act (the “ Additional Divestiture Transactions ”);

WHEREAS, the Company desires to grant to the Parent the Registration Rights (as defined below) for the Retained Shares, subject to the terms and conditions of this Agreement; and

WHEREAS, if there shall be any Retained Shares, then the Parent desires to grant the Company a proxy to vote such Retained Shares in proportion to the votes cast by other stockholders, subject to the terms and conditions of this Agreement.

NOW, THEREFORE, in consideration of the foregoing and the mutual promises, covenants and agreements of the parties hereto, and for other good and valuable consideration the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

ARTICLE I - DEFINITIONS

1.1 Defined Terms . As used in this Agreement, the following terms shall have the following meanings:

“ Affiliate ” shall mean, when used with respect to a specified Person, another Person that controls, is controlled by, or is under common control with the Person specified; provided , however , that, immediately after the Separation, the Company and its Subsidiaries shall not be considered to be “Affiliates” of the Parent, and Parent and its Subsidiaries (other than the Company and its Subsidiaries) shall not be considered to be “Affiliates” of Company. As used herein, “ control ” means the possession, directly or indirectly, of the power to direct or cause the direction of the management and policies of such person, whether through the ownership of voting securities or other interests, by contract or otherwise.

“ Agreement ” has the meaning set forth in the preamble to this Agreement.

“ Board ” means the board of directors of the Company.

“ Business Day ” shall mean any day which is not a Saturday, Sunday or other day on which banking institutions doing business in New York, New York are authorized or obligated by law or required by executive order to be closed.

“ Common Stock ” means the common stock, par value $0.01 per share, of the Company.

“ Company ” has the meaning set forth in the preamble to this Agreement and shall include the Company’s successors by merger, acquisition, reorganization or otherwise.

“ Company Public Sale ” has the meaning set forth in Section 2.2(a) .

“ Debt Exchanges ” means one or more Public Debt Exchanges or Private Debt Exchanges.

“ Debt Securities ” means outstanding debt instruments or securities issued by Parent, including the 6.75% notes due 2011, the 4.00% notes due 2015, the 5.85% notes due 2017, the floating rate notes due 2009, the 5.80 percent notes due 2016, the 6.00% notes due 2017, and the 5.65% notes due 2012.

“ Demand Registration ” has the meaning set forth in Section 2.1(a) .

“ Distribution ” has the meaning set forth in the preamble to this Agreement.

“ Exchange Act ” means the U.S. Securities Exchange Act of 1934, as amended, and any successor thereto, and any rules and regulations promulgated thereunder, all as the same shall be in effect from time to time.

“ Holder ” shall mean the Parent or any of its Subsidiaries, so long as such Person holds any Registrable Securities, and any Person owning Registrable Securities who is a permitted transferee of rights under Section 4.4 .

“ Initiating Holder ” has the meaning set forth in Section 2.1(a) .

“ Loss ” has the meaning set forth in Section 2.7(a) .

“ Parent ” has the meaning set forth in the preamble to this Agreement.

“ Participating Banks ” shall mean such investment banks that engage in any Debt Exchange with the Parent.

“ Private Debt Exchange ” means a private exchange with one or more Participating Banks pursuant to which such Participating Banks shall exchange Debt Securities with Parent for some or all of the Retained Shares in a transaction that is not required to be registered under the Securities Act.

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“ Person ” means any individual, firm, limited liability company or partnership, joint venture, corporation, joint stock company, trust or unincorporated organization, incorporated or unincorporated association, government (or any department, agency or political subdivision thereof) or other entity of any kind, and shall include any successor (by merger or otherwise) of such entity.

“ Piggyback Registration ” has the meaning set forth in Section 2.2(a).

“ Prospectus ” means the prospectus included in any Registration Statement, all amendments and supplements to such prospectus, including post-effective amendments, and all other material incorporated by reference in such prospectus.

“ Public Debt Exchanges ” means a public exchange that is registered under the Securities Act pursuant to which the Parent shall offer Retained Shares in exchange for Debt Securities.

“ Registrable Securities ” means the Retained Shares, and any shares of Common Stock or other securities issued with respect to, in exchange for, or in replacement of such Retained Shares. The term “Registrable Securities” excludes, however, any security (i) the sale of which has been effectively registered under the Securities Act and which has been disposed of in accordance with a Registration Statement, (ii) that has been sold by a Holder in a transaction exempt from the registration and prospectus delivery requirements of the Securities Act under Section 4(1) thereof (including transactions pursuant to Rule 144) such that the further disposition of such securities by the transferee or assignee is not restricted under the Securities Act, or (iii) that have been sold by a Holder in a transaction in which such Holder’s rights under this Agreement are not, or cannot be, assigned.

“ Registration ” means a registration with the SEC of the offer and sale to the public of Common Stock under a Registration Statement. The terms “ Register ” and “ Registering ” shall have a correlative meaning.

“ Registration Expenses ” shall mean all expenses incident to the Company’s performance of or compliance with this Agreement, including all (i) registration, qualification and filing fees; (ii) fees and expenses of compliance with securities or blue sky laws (including reasonable fees and disbursements of counsel in connection with blue sky qualifications within the United States of any Registrable Securities being registered); (iii) printing expenses, messenger, telephone and delivery expenses; (iv) internal expenses of the Company (including all salaries and expenses of employees of the Company performing legal or accounting duties); (v) fees and disbursements of counsel for the

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Company and customary fees and expenses for independent certified public accountants retained by the Company (including the expenses of any comfort letters or costs associated with the delivery by the Company’s independent certified public accountants of comfort letters customarily requested by underwriters); and (vi) fees and expenses of listing any Registrable Securities on any securities exchange on which the shares of Common Stock are then listed and Financial Industry Regulatory Authority registration and filing fees; but excluding any fees or disbursements of the Holder, any underwriting discounts or commissions attributable to the sale of any Registrable Securities, any fees and expenses of the underwriters, any stock transfer taxes, out-of pocket costs and expenses relating to any investor presentations on any “road show” presentations undertaken in connection with marketing of the Registrable Securities and any fees and expenses of counsel to the Holder or the underwriters.

“ Registration Period ” has the meaning set forth in Section 2.1(c) .

“ Registration Rights ” shall mean the rights of the Holders to cause the Company to Register Registrable Securities pursuant to Section 2 .

“ Registration Statement ” means any registration statement of the Company filed with, or to be filed with, the SEC under the rules and regulations promulgated under the Securities Act, including the related Prospectus, amendments and supplements to such registration statement, including post-effective amendments, and all exhibits and all material incorporated by reference in such registration statement.

“ Registration Suspension ” has the meaning set forth in Section 2.1(d) .

“ SEC ” means the U.S. Securities and Exchange Commission.

“ Securities Act ” means the U.S. Securities Act of 1933, as amended, and any successor thereto, and any rules and regulations promulgated thereunder, all as the same shall be in effect from time to time.

“ Shelf Registration Statement ” means a Registration Statement of the Company for an offering to be made on a delayed or continuous basis of Common Stock pursuant to Rule 415 under the Securities Act (or similar provisions then in effect).

“ Underwritten Offering ” means a Registration in which securities of the Company are sold to an underwriter or underwriters on a firm commitment basis for reoffering to the public.

1.2 General Interpretive Principles . Whenever used in this Agreement, except as otherwise expressly provided or unless the context otherwise requires, any noun or pronoun shall be deemed to include the plural as well as the singular and to cover all genders. The name assigned this Agreement and the section captions used herein are for convenience of reference only and shall not be construed to affect the meaning, construction or effect hereof. The table of

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contents and headings contained in this Agreement are for reference purposes only and shall not affect in any way the meaning or interpretation of this Agreement. Whenever the words “ include ,” “ includes ” or “ including ” are used in this Agreement, they shall be deemed to be followed by the words “without limitation.” Unless otherwise specified, the terms “ hereof ,” “ herein ,” “ hereunder ” and similar terms refer to this Agreement as a whole (including the exhibits, schedules and disclosure statements hereto), and references herein to Sections refer to Sections of this Agreement. Except as otherwise indicated, all periods of time referred to herein shall include all Saturdays, Sundays and holidays; provided, however, that if the date to perform the act or give any notice with respect to this Agreement shall fall on a day other than a Business Day, such act or notice may be performed or given timely if performed or given on the next succeeding Business Day. References to a Person are also to its permitted successors and assigns. The parties have participated jointly in the negotiation and drafting of this Agreement and, in the event an ambiguity or question of intent or interpretation arises, this Agreement shall be construed as jointly drafted by the parties, and no presumption or burden of proof shall arise favoring or disfavoring any party by virtue of the authorship of any provision of this Agreement.

ARTICLE II - REGISTRATION RIGHTS

2.1 Registration .

(a) Request . Prior to the fifth anniversary of the Distribution, any Holder(s) of Registrable Securities (collectively, the “ Initiating Holder ”) shall have the right to request that the Company file a Registration Statement with the SEC on the appropriate registration form for all or part of the Registrable Securities held by such Holder, by delivering a written request thereof to the Company specifying the number of shares of Registrable Securities such Holder wishes to register (a “ Demand Registration ”). The Company shall (i) within five days of the receipt of a Demand Registration, give written notice of such Demand Registration to all Holders of Registrable Securities, and (ii) shall use its commercially reasonable efforts to cause the Registration Statement to become effective in respect of each Demand Registration in accordance with the intended method of distribution set forth in the written request delivered by the Holder as expeditiously as possible, and the Company shall use its commercially reasonable efforts to file such Registration Statement within 20 days of receipt of such request. The Company shall include in such Registration all Registrable Securities with respect to which the Company receives, within the 10 days immediately following the receipt by the Holder(s) of such notice from the Company, a request for inclusion in the registration from the Holder(s) thereof. Each such request from a Holder of Registrable Securities for inclusion in the Registration shall also specify the aggregate amount of Registrable Securities proposed to be registered. For purposes of clarification, the Company can satisfy its obligation under this Section 2.1(a) to file a Registration Statement by filing a Shelf Registration Statement and can satisfy its obligation to complete a Demand Registration by filing a Prospectus under an effective Shelf Registration Statement that covers (i) the Registrable Securities requested by the Holders to be registered in accordance with this Section 2.1(a) and (ii) the plan of distribution requested by the participating Holders.

(b) Limitations on Demand Registration Requests . The Holder(s) may collectively make a total of four Demand Registration requests pursuant to Section 2.1(a) (including any rights to Demand Registration transferred pursuant to Section 4.4(a) and any

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rights to Demand Registration made pursuant to any registration rights agreement entered into pursuant to Section 2.5); provided that the Holder(s) may not make more than two Demand Registration requests in any 365-day period. For the avoidance of doubt, if the Parent engages in a Private Debt Exchange as contemplated by Section 2.5 with one or more Participating Banks, each request for a Demand Registration made by a Participating Bank in respect of such Private Debt Exchange pursuant to any registration rights agreement entered into by the Company pursuant to Section 2.5 shall collectively count as one (1) Demand Registration request hereunder (assuming that the Registrable Securities subject to such Private Debt Exchange are included in a single Prospectus). In addition, and notwithstanding anything to the contrary, the Parent and its subsidiaries shall be permitted on a one-time basis to engage in up to three (3) related Private Debt Exchanges within any six (6)-month period during the first year following the date hereof and each Demand Registration request made by the Participating Banks in such Private Debt Exchanges pursuant to its registration rights agreement with the Company shall collectively only count as one (1) Demand Registration request for purposes of the limitation on the number of Demand Registration requests set forth in the first sentence of this Section 2.1(b) (it being understood that, Parent and its subsidiaries shall be permitted to engage in additional Private Debt Exchanges outside such 6-month period, but each Demand Registration request by the Participating Banks for such Private Debt Exchange pursuant to its registration rights agreement with the Company shall count as an additional Demand Registration request for purposes of the limitation on the number of Demand Registration requests set forth in the first sentence of this Section 2.1(b)).

(c) Effective Registration . The Company shall be deemed to have effected a Registration for purposes of this Section 2.1 if the Registration Statement is declared effective by the SEC or becomes effective upon filing with the SEC, and remains effective until the earlier of (i) the date when all Registrable Securities thereunder have been sold and (ii) 60 days from the effective date of the Registration Statement (or from the date the applicable Prospectus is filed with the SEC if the Company is satisfying a request for Demand Registration by filing a Prospectus under an effective Shelf Registration Statement) (the “ Registration Period ”). No Registration shall be deemed to have been effective if the conditions to closing specified in the underwriting agreement, if any, entered into in connection with such Registration are not satisfied by reason of a wrongful act, misrepresentation or breach of such applicable underwriting agreement by the Company. If during the Registration Period, such Registration is interfered with by any stop order, injunction or other order or requirement of the SEC or other governmental agency or court, the Registration Period shall be extended on a day-for-day basis for any period the Holder is unable to complete an offering as a result of such stop order, injunction or other order or requirement of the SEC or other governmental agency or court.

(d) Delay in Filing; Suspension of Registration . If the filing, initial effectiveness or continued use of a Registration Statement at any time would, as reasonably determined in good faith by the Company, (i) have a material detrimental effect on the completion of a transaction currently being negotiated or a plan currently being considered by the Board that would, if completed, be material to the Company and its subsidiaries taken as a whole at the time the right to delay or withhold efforts or suspend sales is exercised (whether or not a final decision has been made to undertake such transaction or plan), or (ii) involve initial or continuing disclosure obligations that are not in the best interests of the Company’s shareholders, the Company may, upon giving prompt written notice of such action to the Holders, delay the

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filing or initial effectiveness of, or suspend use of, the Registration Statement (a “ Registration Suspension ”); provided, however , that the Company shall not be permitted to exercise a Registration Suspension more than three times in any 365-day period and shall not be permitted to exercise a Registration Suspension more than two times in any calendar quarter. Each Registration Suspension shall not exceed 30 days. Notwithstanding the foregoing, no such delay shall exceed such number of days that the Company determines in good faith to be reasonably necessary. In the case of a Registration Suspension, the Holders agree to suspend use of the applicable Prospectus in connection with any sale or purchase of, or offer to sell or purchase, Registrable Securities, upon receipt of the notice referred to above (which may be delivered orally). The Company shall (i) immediately notify the Holders upon the termination of any Registration Suspension, (ii) amend or supplement the Prospectus, if necessary, so it does not contain any untrue statement or omission therein, and (iii) furnish to the Holders such numbers of copies of the Prospectus as so amended or supplemented as the Holders may reasonably request. The effectiveness period for any Demand Registration for which the Company has exercised a Registration Suspension shall be increased by the period of time such Registration Suspension is in effect.

(e) Underwritten Offering . If the Initiating Holder so indicates at the time of its request pursuant to Section 2.1(a) , such offering of Registrable Securities shall be in the form of an Underwritten Offering and the Company shall include such information in its written notice to the Holders required under Section 2.1(a) . In the event that the Initiating Holder intends to distribute the Registrable Securities by means of an Underwritten Offering, the right of any Holder to include Registrable Securities in such registration shall be conditioned upon such Holder’s participation in such underwriting and the inclusion of such Holder’s Registrable Securities in the underwriting to the extent provided herein. The Holders of a majority of the outstanding Registrable Securities being included in any Underwritten Offering shall select the underwriter(s) for such Underwritten Offering; provided, however , that such underwriter(s) must be reasonably acceptable to the Company.

(f) Priority of Securities Registered . If the managing underwriter or underwriters of a proposed Underwritten Offering of Registrable Securities included in a Registration pursuant of this Section 2.1 , informs the Holders with Registrable Securities in such Registration of such class of Registrable Securities in writing that, in its or their opinion, the number of securities requested to be included in such Registration exceeds the number which can be sold in such offering without being likely to have a significant adverse effect on the price, timing or distribution of the securities offered or the market for the securities offered, the Holders shall have the right to (i) request the number of Registrable Securities to be included in such Registration be allocated pro rata among the Holders, including the Initiating Holder, to the extent necessary to reduce the total number of Registrable Securities to be included in such offering to the number recommended by the managing underwriter or underwriters; provided that any securities thereby allocated to a Holder that exceed such Holder’s request shall be reallocated among the remaining Holders in like manner or (ii) notify the Company in writing that the Registration Statement shall be abandoned or withdrawn, in which event the Company shall abandon or withdraw such Registration Statement. In the event a Holder notifies the Company that such Registration Statement shall be abandoned or withdrawn said Holder shall not be deemed to have requested a Demand Registration pursuant to Section 2.1(a) and the Company shall not be deemed to have effected a Demand Registration pursuant to Section 2.1(b) .

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If the amount of Registrable Securities to be underwritten has not been so limited, the Company and other holders may include shares of Common Stock for its own account (or for the account of other holders) in such Registration if the underwriter(s) so agree and to the extent that, in the opinion of such underwriter(s), the inclusion of such additional amount will not adversely affect the offering of the Registrable Securities included in such Registration.

2.2 Piggyback Registrations .

(a) Participation . Prior to the earlier to occur of the fifth anniversary of the Distribution or the date on which the Registrable Securities then held by the Holder(s) represents less than five percent (5%) of the Company’s then issued and outstanding Common Stock, if the Company proposes to file a Registration Statement under the Securities Act with respect to any offering of its Common Stock for its own account and/or for the account of any other Persons (other than (i) a Registration under Section 2.1 hereof, (ii) a Registration pursuant to a Registration Statement on Form S-8 or Form S-4 or similar forms that relate to a transaction subject to Rule 145 under the Securities Act, (iii) any form that does not include substantially the same information, other than information relating to the selling holders or their plan of distribution, as would be required to be included in a Registration Statement covering the sale of Registrable Securities, (iv) in connection with any dividend reinvestment or similar plan, (v) for the sole purpose of offering securities to another entity or its security holders in connection with the acquisition of assets or securities of such entity or any similar transaction or (vi) a Registration in which the only Common Stock being registered is Common Stock issuable upon conversion of debt securities which are also being registered) (a “ Company Public Sale ”), then, as soon as practicable (but in no event less than 15 days prior to the proposed date of filing such Registration Statement), the Company shall give written notice of such proposed filing to each Holder, and such notice shall offer such Holders the opportunity to Register under such Registration Statement such number of Registrable Securities as each such Holder may request in writing (a “ Piggyback Registration ”). Subject to Section 2.2(b) and Section 2.2(c) , the Company shall include in such Registration Statement all such Registrable Securities which are requested to be included therein within 5 Business Days after the receipt of any such notice; provided, however , that if, at any time after giving written notice of its intention to Register any securities and prior to the effective date of the Registration Statement filed in connection with such Registration, the Company shall determine for any reason not to Register or to delay Registration of such securities, the Company may, at its election, give written notice of such determination to each such Holder and, thereupon, (i) in the case of a determination not to Register, shall be relieved of its obligation to Register any Registrable Securities in connection with such Registration, without prejudice, however, to the rights of any Holder to request that such Registration be effected as a Demand Registration under Section 2.1 , and (ii) in the case of a determination to delay Registering, shall be permitted to delay Registering any Registrable Securities, for the same period as the delay in Registering such other shares of Common Stock. No Registration effected under this Section 2.2 shall relieve the Company of its obligation to effect any Demand Registration under Section 2.1 . If the offering pursuant to such Registration Statement is to be underwritten, then each Holder making a request for a Piggyback Registration pursuant to this Section 2.2(a) shall, and the Company shall use commercially reasonable efforts to coordinate arrangements with the underwriters so that each such Holder may, participate in such Underwritten Offering. If the offering pursuant to such Registration Statement is to be on any other basis, then each Holder making a request for a Piggyback Registration pursuant to this

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Section 2.2(a) shall, and the Company shall use commercially reasonable efforts to coordinate arrangements so that each such Holder may, participate in such offering on such basis. For purposes of clarification, the Company’s filing of a Shelf Registration Statement shall not be deemed to be a Company Public Sale; provided, however , that any prospectus supplement filed pursuant to a Shelf Registration Statement with respect to an offering of the Company’s Common Stock for its own account and/or for the account of any other Persons will be a Company Public Sale unless such offering qualifies for an exemption from the Company Public Sale definition in this Section 2.2(a).

(b) Right to Withdraw . Each Holder shall have the right to withdraw such Holder’s request for inclusion of its Registrable Securities in any Underwritten Offering pursuant to this Section 2.2(a) at any time prior to the execution of an underwriting agreement with respect thereto by giving written notice to the Company of such Holder’s request to withdraw and, subject to the preceding clause, each Holder shall be permitted to withdraw all or part of such Holder’s Registrable Securities from a Piggyback Registration at any time prior to the effective date thereof.

(c) Priority of Piggyback Registration . If the managing underwriter or underwriters of any proposed Underwritten Offering of a class of Registrable Securities included in a Piggyback Registration informs the Company and Holders in writing that, in its or their opinion, the number of securities of such class which such Holder and any other Persons intend to include in such offering exceeds the number which can be sold in such offering without being likely to have an adverse effect on the price, timing or distribution of the securities offered or the market for the securities offered, then the securities to be included in such Registration shall be (i) first, all securities of the Company and any other Persons (other than the Company’s executive officers and directors) for whom the Company is effecting the Registration, as the case may be, proposes to sell, (ii) second, the number of Registrable Securities of such class that, in the opinion of such managing underwriter or underwriters, can be sold without having such adverse effect, with such number to be allocated pro rata among the Holders that have requested to participate in such Registration based on the relative number of Registrable Securities of such class requested by such Holder to be included in such sale ( provided that any securities thereby allocated to a Holder that exceed such Holder’s request shall be reallocated among the remaining requesting Holders in like manner), subject to any superior contractual rights of other holders,(iii) third, the number securities of executive officers and directors for whom the Company is effecting the Registration, as the case may be, with such number to be allocated pro rata among the executive officers and directors, and (iv) fourth, any other securities eligible for inclusion in such Registration, allocated among the holders of such securities in such proportion as the Company and those holders may agree.

(d) Black-Out Periods . In the event of a public sale of the Company’s equity securities by the Company in an Underwritten Offering, whether or not the Holders participate therein, the Holders hereby agree, and the Company agrees that is shall cause its executive officers and directors to agree, if requested by the managing underwriter or underwriters in such Underwritten Offering, not to effect any sale or distribution (including any offer to sell, contract to sell, short sale or any option to purchase) of any securities (except, in each case, as part of the applicable Registration, if permitted hereunder) that are the same as or similar to those being Registered in connection with such Company Public Sale, or any securities convertible into or

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