INVESTOR RIGHTS AGREEMENT

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                                                                         EX-10.4

                            INVESTOR RIGHTS AGREEMENT

     This Investor Rights Agreement (the "AGREEMENT") is made as of April 21,
2006, by and among Third Wave Technologies Japan, K.K., a Japanese corporation
(the "COMPANY"), Third Wave Technologies, Inc., a Delaware corporation (the
"PARENT"), and the entities listed on Exhibit A attached hereto (each, an
"INVESTOR," and collectively, the "INVESTORS").

                                    RECITALS

     A. WHEREAS: The Parent currently owns all of the outstanding capital stock
issued by the Company.

     B. WHEREAS: The Investors intend to purchase from the Company shares of its
Series A Preferred Stock, pursuant to the Series A Preferred Stock Purchase
Agreement between the Company and the Investors, dated of even date herewith
(the "SERIES A PURCHASE AGREEMENT").

     C. WHEREAS: In consideration for the Investors' investments in the Company,
the Investors, the Company and the Parent have agreed to enter into this
Agreement.

     NOW, THEREFORE, in consideration of the mutual promises herein contained,
and other consideration, the receipt and adequacy of which hereby is
acknowledged, the parties hereto agree as follows:

                                    SECTION 1

                               CERTAIN DEFINITIONS

     For purposes of this Agreement, the following terms have the following
meanings:

     1.1 "AFFILIATE" means any business entity which controls, is controlled by
or is under common control of a party and, for the purposes of this definition,
a business entity shall be deemed to "control" another business entity if it
owns, directly or indirectly, at least twenty percent (20%) of the shares of
such business entity or any other comparable equity or ownership interest with
respect to a business entity other than a company;

     1.2 "CHANGE OF CONTROL" means (i) a merger or consolidation of the Company
or Parent, as the case may be, or other transaction where the Company's
shareholders or the Parent's stockholders, as the case may be, immediately
before the transaction do not hold more than fifty percent (50%) of the
outstanding voting shares of the surviving entity after such transaction, or
(ii) a sale, lease, transfer or other disposition of all or substantially all of
the assets of the Company or the Parent, as the case may be.

     1.3 "ELIGIBLE INVESTORS" shall mean the Shareholders other than the Seller.

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     1.4 "CO-SALE SHARE" means, as to each Eligible Investor's Right of Co-Sale,
the percentage determined by dividing (i) the number of shares of Stock held by
the Eligible Investor by (ii) the number of shares of Stock held by the Seller
and all Eligible Investors participating in the Right of Co-Sale pursuant to
Section 6 hereof.

     1.5 "NEW SECURITIES" shall have the meaning in Section 3.2.

     1.6 "PREEMPTIVE RIGHT" means the preemptive right provided to the
Shareholders in Section 3 of this Agreement.

     1.7 "QUALIFIED IPO" means the Company's sale of its common stock in a bona
fide, firm commitment underwriting pursuant to a registration statement filed
with the Japanese Financial Services Agency, with aggregate proceeds to the
Company of at least Y1,000,000,000 and a per share price to the public of at
least two times the price paid by the Investors for the Company's Series A
Preferred Stock under the Series A Purchase Agreement.

     1.8 "RIGHT OF CO-SALE" means the right of co-sale provided to the Eligible
Investors in Section 6 of this Agreement.

     1.9 "RIGHT OF FIRST REFUSAL" means the right of first refusal provided to
the Company and the Eligible Investors in Section 5 of this Agreement.

     1.10 "SERIES A PREFERRED STOCK" means the Company's Series A Preferred
Stock.

     1.11 "SERIES A PURCHASE AGREEMENT" shall have the meaning in the Recitals.

     1.12 "SELLER" means the Parent or any Investor proposing to Transfer Stock.

     1.13 "SHAREHOLDERS" means the Parent and the Investors.

     1.14 "STOCK" means and includes all common stock and preferred stock of the
Company.

     1.15 "TRANSFER" means and includes any sale, assignment, encumbrance,
hypothecation, pledge, conveyance in trust, gift or other transfer or
disposition of any kind, including but not limited to transfers to receivers,
levying creditors, trustees or receivers in bankruptcy proceedings or general
assignees for the benefit of creditors, whether voluntary or by operation of
law, directly or indirectly, except:

          (a) any transfers by the Parent in connection with a Change of Control
of the Parent;

          (b) any transfers by any Shareholder to its Affiliate other than
transfers between TWJ and TWT;

          (c) any bona fide gift, provided that the Seller shall inform the
Eligible Investors of such gift prior to effecting it and provided that the
pledgee, transferee or donee or other recipient executes a counterpart copy of
this Agreement and becomes bound thereby as was the Seller;


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          (d) by operation of law; or

          (e) any transfer to the Company or an Eligible Investor pursuant to
the terms of this Agreement.

     1.16 "BUSINESS DAY" means any day from Monday to Friday, except for the
holidays on which commercial banking institutions in either Japan or the State
of Wisconsin in the US are authorized or obligated by law to be closed.

                                    SECTION 2

                        INFORMATION AND INSPECTION RIGHTS

     2.1 INFORMATION RIGHTS. So long as at least fifty percent (50%) of the
Series A Preferred Stock remains outstanding and the Investors continue to own
at least eighty percent (80%) of the shares of such Series A Preferred Stock (or
shares of common stock issued upon conversion of the Series A Preferred Stock)
held by the Investors as of the date of this Agreement, the Company will furnish
the following reports to any Investor:

          (a) within one hundred twenty (120) days after the end of each fiscal
year of the Company, a consolidated balance sheet of the Company and its
subsidiaries, if any, as at the end of such fiscal year, and consolidated
statements of income and cash flows of the Company and its subsidiaries, if any,
for such year, prepared in accordance with generally accepted accounting
principles in Japan consistently applied, certified by independent public
accountants of recognized national standing selected by the Company.

          (b) within forty-five (45) days after the end of the first, second,
and third quarterly accounting periods in each fiscal year of the Company, an
unaudited consolidated balance sheet of the Company and its subsidiaries, if
any, as of the end of each such quarterly period, and unaudited consolidated
statements of income and cash flows of the Company and its subsidiaries, if any,
for such period.

          (c) within fifteen (15) days after the end of each month, an unaudited
consolidated balance sheet of the Company and its subsidiaries, if any, as of
the end of such monthly period, and consolidated statements of income and cash
flows of the Company and its subsidiaries, if any, for such period.

          (d) within forty-five (45) days after the end of each fiscal quarter,
an up-to-date capitalization table, including the names of each shareholder and
option or warrant holder and the number of shares, options or warrants held by
each such holder, certified by the management member chiefly responsible for the
finances of the Company.

          (e) at least thirty (30) days prior to the beginning of each fiscal
year, an operating plan for such fiscal year, including consolidated capital and
operating expense budgets, cash flow projections and income and loss projections
for the Company and its subsidiaries in respect of such


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fiscal year, all itemized in reasonable detail and prepared on a monthly basis,
and, promptly after preparation, any revisions to any of the foregoing.

     2.2 INSPECTION RIGHTS. So long as at least fifty percent (50%) of the
Series A Preferred Stock remains outstanding and the Investors continue to own
at least eighty percent (80%) of the shares of such Series A Preferred Stock (or
shares of common stock issued upon conversion of the Series A Preferred Stock)
held by the Investors as of the date of this Agreement, the Company will afford
to each Investor that owns at least fifteen percent (15%) of the then issued and
outstanding Series A Preferred Stock, and to each such Investor's accountants
and counsel, reasonable access during normal business hours and with reasonable
advance notification, to all of the Company's respective properties, books and
records. Each such Investor shall have such other reasonable access, with
reasonable advance notification, to management and information as is necessary
for it to comply with applicable laws and regulations and reporting obligations.
The Company shall not be required to disclose details of contracts with or work
performed for specific customers and other business partners where to do so
would violate confidentiality obligations to those parties. The Investors may
exercise their rights under this Section 2.2 only for purposes reasonably
related to their interests under this Agreement and related agreements. The
rights granted pursuant to this Section 2.2 may not be assigned or otherwise
conveyed by the Investors or by any subsequent transferee of any such rights
without the prior written consent of the Company.

     2.3 CONFIDENTIALITY. Anything in Section 2 to the contrary notwithstanding,
no Investor by reason of this Agreement shall have access to any trade secrets
or confidential information of the Company. Each Investor hereby agrees to hold
in the strictest confidence and trust, and to take reasonable precautions to
prevent the unauthorized use or disclosure of, any confidential information
provided pursuant to this Agreement. The Company shall not be required to comply
with any obligation under this Section 2 in respect of any Investor whom the
Company reasonably determines to be a competitor or an officer, employee,
director or holder of more than ten percent (10%) of the stock of a competitor.

     2.4 TERMINATION OF INFORMATION AND INSPECTION RIGHTS. Each Investor's
information and inspection rights set forth in this Section 2 shall terminate in
accordance with Section 10.1 hereof.

                                    SECTION 3

                                PREEMPTIVE RIGHTS

     3.1 PREEMPTIVE RIGHTS TO SHAREHOLDERS. The Company hereby grants to the
Shareholders, the preemptive right to purchase a pro rata share of New
Securities (as defined in Section 3.2) which the Company may, from time to time,
propose to sell and issue (the "PREEMPTIVE RIGHT"). A Shareholder's pro rata
share, for purposes of the Preemptive Right, is the ratio of the number of
shares of common stock owned by such Shareholder immediately prior to the
issuance of New Securities, assuming full conversion of the Shares and exercise
of any option or warrant held by said Shareholder, to the total number of shares
of common stock outstanding immediately prior to the issuance of New Securities,
assuming full conversion of the Shares and exercise of all outstanding


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convertible securities, rights, options and warrants to acquire common stock of
the Company. Each Shareholder shall have a right of over-allotment such that if
any Shareholder fails to exercise its right hereunder to purchase its pro rata
share of New Securities, the other Shareholders may purchase the non-purchasing
Shareholder's portion on a pro rata basis within ten (10) Business Days from the
Purchase Deadline (as defined below).

     3.2 NEW SECURITIES. "NEW SECURITIES" shall mean any capital stock
(including common stock and/or preferred stock) of the Company whether now
authorized or not, and securities of any type whatsoever that are, or may
become, convertible into capital stock; provided that the term "New Securities"
does not include:

          (a) securities purchased under the Series A Purchase Agreement;

          (b) shares of common stock issued or issuable upon conversion of
shares of preferred stock;

          (c) shares of common stock issued or issuable upon exercise of any
warrants issued pursuant to the Series A Purchase Agreement;

          (d) shares of common stock issued or issuable (including securities
convertible into or exercisable for common stock) to officers, directors and
employees of, or consultants to, the Company pursuant to stock grants, option
plans, purchase plans or other stock incentive programs or similar arrangements
approved by the Board of Directors of the Company, or upon exercise of options
or warrants granted to such parties pursuant to any such plan or arrangement;

          (e) shares of common stock issued upon the exercise or conversion of
options or convertible securities of the Company outstanding as of the date of
this Agreement, as amended, or that are subsequently issued pursuant to the
carve-outs of Sections 3.2(a)-(j) hereof, as amended;

          (f) shares of common stock issued or issuable (including securities
convertible into or exercisable for common stock) as a dividend or distribution
on preferred stock, or pursuant to any event for which adjustment is made to the
number of shares of common stock outstanding, including, without limitation, a
stock split, stock dividend, subdivision of shares of common stock or other
similar transaction, or pursuant to any other event for which adjustment is made
pursuant to the Articles of Incorporation of the Company (the "ARTICLES");

          (g) shares of common stock issued in a registered public offering
under the Securities and Exchange Law, as amended, pursuant to which all
outstanding shares of preferred stock are automatically converted into common
stock;

          (h) shares of common stock issued or issuable (including securities
convertible into or exercisable for common stock) pursuant to the acquisition of
another entity by the Company by merger, purchase of equity, purchase of
substantially all of the assets, or other reorganization, or pursuant to a joint
venture agreement, provided, that such issuances are approved by the Board of
Directors of the Company;


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          (i) shares of common stock issued or issuable (including securities
convertible into or exercisable for common stock) to lenders, service providers,
equipment lessors or other financial institutions pursuant to a commercial
leasing, debt financing, service or consulting transaction, each as approved by
the Board of Directors of the Company; and

          (j) shares of common stock issued or issuable (including securities
convertible into or exercisable for common stock) in connection with sponsored
research, collaboration, license, development, OEM, marketing, acquisition, or
other similar agreements or strategic transactions approved by the Board of
Directors of the Company.

     3.3 NOTICE OF EXERCISE. In the event the Company proposes to undertake an
issuance of New Securities, it shall give each Shareholder written notice of its
intention, describing the type of New Securities, and their price and the
general terms upon which the Company proposes to issue the same. Each
Shareholder shall have ten (10) Business Days after any such notice is mailed or
delivered (the "PURCHASE DEADLINE") to agree to purchase such Shareholder's pro
rata share of such New Securities for the price and upon the terms specified in
the notice by giving written notice to the Company and stating therein the
quantity of New Securities to be purchased.

     3.4 FAILURE TO EXERCISE. In the event the Shareholders fail to exercise
fully their Preemptive Rights within said ten (10) Business Day period and after
the expiration of the additional ten (10) Business Day period for the exercise
of the over-allotment provisions of Section 3.1, the Company shall have ninety
(90) days thereafter to sell or enter into an agreement (pursuant to which the
sale of New Securities covered thereby shall be closed, if at all, within ninety
(90) days from the date of said agreement) to sell the New Securities respecting
which the Shareholders' Preemptive Rights set forth in Section 3.1 were not
exercised, at a price and upon terms no more favorable to the purchasers thereof
than specified in the Company's notice to Shareholders pursuant to Section 3.3.
In the event the Company has not sold the New Securities within such ninety (90)
day period, the Company shall not thereafter issue or sell any New Securities,
without first again offering such securities to the Shareholders in the manner
provided in Section 3.1 above.

     3.5 ASSIGNMENT OF PREEMPTIVE RIGHT. The Preemptive Right may not be
assigned or transferred, except that (i) such right is assignable by each
Shareholder to the Affiliates of any such Shareholder, and (ii) such right is
assignable between and among any of the Shareholders.

     3.6 INAPPLICABILITY AND TERMINATION OF PREEMPTIVE RIGHT. The Preemptive
Right shall not be applicable to the Company's Qualified IPO, and shall
terminate in accordance with Section 10.1 hereof.

                                    SECTION 4

                            RESTRICTIONS ON TRANSFER

     4.1 GENERAL. Before a Seller may Transfer any Stock, securities convertible
into Stock, or Stock issued upon conversion of any securities held by the Seller
as of the date hereof (as adjusted for any stock dividends, stock splits,
recapitalizations and the like), the Company or its assignee(s) and the


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Eligible Investors shall have a Right of First Refusal to purchase such Stock on
the terms and conditions set forth herein.

     4.2 NOTICE OF PROPOSED TRANSFER. Prior to the Seller Transferring any
Stock, the Seller shall deliver to the Company and the Eligible Investors a
written notice (the "TRANSFER NOTICE") stating: (i) the Seller's bona fide
intention to sell or otherwise Transfer such Stock (the "OFFERED SHARES"); (ii)
the name, address and phone number of each proposed purchaser or other
transferee ("PROPOSED TRANSFEREE"); (iii) the aggregate number of Offered Shares
to be Transferred to each Proposed Transferee; (iv) the bona fide cash price or
other consideration for which the Seller proposes to Transfer the Offered Shares
(the "OFFERED PRICE"); (v) each Eligible Investor's right to exercise either its
Right of First Refusal or its Right of Co-Sale (but not both rights) with
respect to the Offered Shares; and (vi) a deadline, consistent with the terms of
this Agreement, within which the Company and Eligible Investors must exercise
such rights.

                                    SECTION 5

                             RIGHT OF FIRST REFUSAL

     5.1 TRANSFER OF SHARES TO THE COMPANY. The Company may elect itself as the
transferee of the Offered Shares, provided that the Company shall purchase all
but not less than all of the Offered Shares and shall give written notice of
such election to the Seller within fifteen (15) Business Days after the date on
which the Transfer Notice is, pursuant to Section 11.1 hereof, deemed to have
been delivered to the Company and the Eligible Investors (the "INITIAL REFUSAL
PERIOD").

     5.2 INITIAL EXERCISE BY THE ELIGIBLE INVESTORS. Subject to the limitations
of this Section 5.2, the Eligible Investors and their Affiliates appointed by
the Eligible Investors shall have the Right of First Refusal to purchase all or
any part of the Offered Shares should the Company not elect itself as the
transferee of the Offered Shares pursuant to Section 5.1 hereof; provided that
each Eligible Investor so electing gives written notice of the exercise of such
right to the Seller within the Initial Refusal Period. Upon the earlier to occur
of (a) the termination of the Initial Refusal Period and (b) the time when the
Seller has received written confirmation from the Company regarding its exercise
of its Right First Refusal, the Eligible Investors' Rights of First Refusal
shall expire. To the extent that the Company elects not to purchase the Offered
Shares, the Company shall allocate the Offered Shares to the Eligible Investors,
and shall give written notice thereof to the Seller within the Initial Refusal
Period. To the extent that the aggregate number of shares that the Eligible
Investors desire to purchase exceeds the number of Offered Shares, each Eligible
Investor will be entitled to purchase a fraction of the Offered Shares, the
numerator of which shall be the number of shares of common stock (assuming
conversion of all securities then outstanding that are convertible into common
stock) owned by such Eligible Investor on the date of the Transfer Notice and
the denominator of which shall be the number of shares of Stock held by all
Eligible Investors exercising their Right of First Refusal. Within five (5)
Business Days after the expiration of the Initial Refusal Period (the
"CONFIRMATION PERIOD"), the Seller will give written notice to the Company and
each Eligible Investor specifying the number of Offered Shares that was
subscribed by the Company or the Eligible Investors exercising their Rights of
First Refusal, as the case may be (the "CONFIRMATION NOTICE"). The Confirmation
Notice shall specify the number of Offered Shares to be purchased by the Company
or those Eligible Investors who are exercising their Rights of First Refusal. If
the Company does not elect itself as the transferee of the


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Offered Shares, the Confirmation Notice shall also specify the number of Offered
Shares not purchased, if any, and list each Participating Investor's (as defined
in Section 5.3 hereof) share of the Offered Shares. This Right of First Refusal
shall not apply with respect to Offered Shares sold by the Investors under the
Right of Co-Sale.

     5.3 SUBSEQUENT EXERCISE BY THE ELIGIBLE INVESTORS. Each Eligible Investor
electing to exercise its Right of First Refusal to purchase at least its full
pro rata share of the Offered Shares under Section 5.2 hereof (a "PARTICIPATING
INVESTOR") shall have a right of reallotment such that if, after the Eligible
Investors exercise their respective Rights of First Refusal, there remain any
Offered Shares that are not purchased by the Eligible Investors within the
Initial Refusal Period, then each such Participating Investor may elect to
purchase all (or any portion of) such Participating Investor's pro rata share of
the Offered Shares not previously purchased. For the purpose of the preceding
sentence, each Participating Investor's pro rata share shall be a fraction of
the Offered Shares not previously purchased, the numerator of which shall be the
number of shares of common stock (assuming conversion of all securities then
outstanding that are convertible into common stock) owned by such Participating
Investor on the date of the Transfer Notice and the denominator of which shall
be the total number of shares of common stock (assuming conversion of all
securities then outstanding that are convertible into common stock) held by all
Participating Investors on the date of the Transfer Notice. Each Eligible
Investor exercising its right pursuant to this Section 5.3 shall do so by giving
written notice to the Seller within seven (7) Business Days after delivery of
the Confirmation Notice to such Eligible Investor pursuant to Section 11.1 (the
"SUBSEQUENT REFUSAL PERIOD").

     5.4 PURCHASE PRICE. The purchase price for the Offered Shares to be
purchased by the C