PRAXAIR, INC. SUPPLEMENTAL RETIREMENT INCOME PLAN

Exhibit 10.05a

PRAXAIR, INC.

SUPPLEMENTAL RETIREMENT INCOME PLAN A

(EFFECTIVE JANUARY 1, 2008)

PRAXAIR, INC.

SUPPLEMENTAL RETIREMENT INCOME PLAN A

General

This Supplemental Retirement Income Plan A (the “Plan”) is maintained by Praxair, Inc. (the “Corporation”), is completely separate from the Praxair Pension Plan (the “Pension Plan”), and is not funded or qualified for special tax treatment under the Internal Revenue Code of 1986, as amended (the “Code”). The purpose of this Plan is to restore retirement benefits to those Pension Plan participants, and to the spouses or beneficiaries of such participants, whose retirement benefits under the Pension Plan are, or will be, reduced by the limitations imposed by Section 401(a)(17) of the Code, as from time to time amended (collectively referred to herein as “Participants”).

This Plan operates in conjunction with the Pension Plan, the Praxair, Inc. Equalization Benefit Plan (the “EBP”) and the Praxair, Inc. Supplemental Retirement Income Plan B (the “SRIP B”) to provide retirement benefits to Participants. Each of these four plans must be read together in the following order to determine the total Praxair retirement benefit payable to, or on behalf of, a Participant:

In no event shall any benefit payable to or on behalf of a Participant under this Plan duplicate the benefit payable to or on behalf of such Participant under the Pension Plan, the EBP and/or the SRIP B.

This Plan is effective January 1, 2008.

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ARTICLE I

SRIP A Benefits

Section 1 . Each Participant shall be designated as either an Account-Based Participant or a Traditional-Design Participant. This designation shall be consistent with such Participant’s method of benefit accrual under the Pension Plan.

Any Participant in the Pension Plan, or such Participant’s surviving spouse or beneficiary, shall be entitled to a benefit, payable hereunder in accordance with this Plan, calculated under either A or B below (referred to herein as the “SRIP A Benefit”).

A. Amount of SRIP A Benefit for Traditional-Design Participants . The SRIP A Benefit hereunder payable to a Traditional-Design Participant or his or her surviving spouse shall be equal to the excess of (a) minus (b), if any, determined as of termination of employment, where (a) and (b) are defined as follows:

(a) equals the amount of such Participant’s or surviving spouse’s annual benefit under the Pension Plan computed under the provisions of the Pension Plan without regard to the limitations of Code Sections 415 and 401(a)(17); and

(b) equals the amount of such Participant’s or surviving spouse’s annual benefit actually payable under the Pension Plan and the EBP.

B. Amount of SRIP A Benefit for Account-Based Participants . The SRIP A Benefit hereunder payable to or on behalf of an Account-Based Participant shall be equal to the excess of (a) minus (b), if any, determined as of termination of employment, where (a) and (b) are defined as follows:

(a) equals the Account-Based Account (as defined in the Pension Plan) which the Participant would have had at such time under the Pension Plan as if such amounts had been determined without applying the limitations of Code Sections 415 and 401(a)(17); and

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(b) equals the actual Account-Based Account which the Participant has at such time under the Pension Plan plus the actual amount of the notional account which the Participant has at such time under the EBP.

C. Provisions Common to All Participants .

(a) If a Participant satisfies the requirements for a survivor’s benefit, the amount of the SRIP A Benefit which such Participant would otherwise have received shall be reduced by applying the same factor used in the Pension Plan in connection with survivor’s benefits.

(b) The amount of the SRIP A Benefit payable to the eligible survivor of a Participant shall be calculated in the same manner that such survivor’s benefit is calculated under the Pension Plan.

(c) With respect to any benefit hereunder payable to a “spouse,” the determination of whether a person constitutes an eligible spouse shall be made under the same criteria as apply under the Pension Plan.

ARTICLE II

Vesting

Section 1 . Except as otherwise provided herein, a Participant will be vested in such Participant’s right to receive SRIP A benefits in the same manner and to the same extent as provided under the Pension Plan.

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ARTICLE III

Benefit Payments

Section 1 . For Traditional-Design Participants, payments shall be made as follows:

(a) For Traditional-Design Participants who terminate employment at a time when they would be immediately eligible to commence a benefit under the Pension Plan, a single life annuity (or a 50% joint and survivor annuity for such Participants who are married at the time of their termination of employment) will commence to be paid as of the first of the month coincident with or next following such termination, and a lump sum payment of all remaining SRIP A Benefits due hereunder shall be made on or about July 1 of the year immediately following the year of such termination (the year of termination is hereinafter referred to as the “Termination Year”). Where such Participant has commenced a 50% joint and survivor annuity, and such Participant’s spouse dies during the annuity payment period, the Participant’s SRIP A Benefit will be increased to eliminate the cost of the survivor benefit. Notwithstanding the foregoing, if such Participant is a Specified Employee (as such term is defined in Code Section 409A) no annuity benefits shall be paid during the six month period after the Participant’s termination of employment (the “Delay Period”), and at the conclusion of the Delay Period any annuity benefits which would otherwise have been paid during the Delay Period shall be paid in a single sum which shall include interest at the interest rate used for determining Actuarial Equivalence, as then in effect under the Pension Plan. Annuity benefits shall then commence and continue until a lump sum payment is due pursuant to the first sentence of this paragraph.

(b) For Traditional-Design Participants who terminate employment at a time when they would not be immediately eligible to commence a benefit under the Pension Plan, a lump sum payment of all SRIP A Benefits due hereunder, (taking into account the value of the 50%

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joint and survivor form of benefit if the Participant is married at the time of termination of employment), shall be made on or about July 1 of the year immediately following the Termination Year. If such Participant’s spouse dies prior to the date of such lump sum payment, the Participant’s SRIP A Benefit shall not be reduced to reflect the cost of the survivor benefit.

(c) Lump sum payments shall be calculated using a discount rate equal to the 10 year Aaa municipal bond rate as published by Moody’s or a similar rating service for the third month prior to the month payments commence.

(d) Notwithstanding the foregoing, a Traditional-Design Participant described in Article III, Section 1(a) may elect to receive a lump sum payment of such Participant’s remaining unpaid SRIP A Benefit in January of the year following the Termination Year, provided that such election must be made during 2008 by a Participant who terminates employment on or after January 1, 2008 but before July 1, 2008, and relates to a lump sum benefit otherwise not scheduled to be paid in 2008.

Section 2 . (a) For Account-Based Participants who terminate employment on or after November 1 of a year and prior to May 1 of the following year, a lump sum of their SRIP A Benefit shall be paid on or about July 1 of that following year. For Account-Based Participants who terminate employment on or after May 1 and prior to November 1 of a year, a lump sum of their SRIP A Benefit shall be paid on or about January 1 of the following year. (By way of example, an Account-Based Participant who terminates employment in December, 2008, and an Account-Based Participant who terminates employment in April, 2009, would each receive a lump sum in July, 2009. An Account-Based Participant who terminates employment in June, 2009, would receive a lump sum in January, 2010.) Notwithstanding the foregoing, if such

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Participant is a Specified Employee (as such term is defined in Code Section 409A) no payment shall be made until the later of the date determined above and the date which is six months after the Participant’s termination of employment.

(b) Such lump sum payment shall be calculated utilizing the factors described for lump sum payments under Section 5.7(b) (or any successor provision governing calculations of Account-Based lump sums) of the Pension Plan.

Section 3 . In the event of a Change in Control, all SRIP A Benefits not yet paid under this Plan shall become immediately vested and shall be paid in a lump sum payment, calculated as otherwise described herein, as soon as administratively possible following the date of such Change in Control, but no later than 90 days after such date. For this purpose, Change in Control shall mean the occurrence of any one of the following events with respect to the Corporation:

(a) during a 12-month period, a majority of the individuals who constitute the Corporation’s Board of Directors are replaced by directors whose appointment or election is not endorsed by a majority of the members of the Board before the date of the appointment or election;

(b) any one person, or more than one person acting as a group, becomes owner as defined in Section 318(a) of the Internal Revenue Code of 1986 (the “Code”) (or has become owner during the 12-month period ending on the date of the most recent acquisition by such person or group), of stock of the Corporation possessing 30 percent or more of the total voting power of the stock of the Corporation; provided, however, that the event described in this paragraph (ii) shall not be deemed to be a Change in Control by virtue of any of the following

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acquisitions: (A) by the Corporation or any of its subsidiaries, (B) by any employee benefit plan sponsored or maintained by the Corporation or any of its subsidiaries, or (C) by any underwriter temporarily holding securities pursuant to an offering of such securities.

(c) any one person, or more than one person acting as a group, acquires (or has acquired during the 12-month period ending on the date of the most recent acquisition by such person or group) assets from the Corporation that have a total gross fair market value equal to or more than 80 percent of the total gross fair market value of all of the assets of the Corporation immediately prior to such acquisition(s); provided, however, that a transfer of assets by the Corporation is not treated as a Change in Control if the assets are transferred to: (A) a shareholder of the Corporation (immediately before the asset transfer) in exchange for or with respect to its stock; (B) an entity, 50 percent or more of the total value or voting power of which is owned, directly or indirectly, by the Corporation; (C) a person, or more than one person acting as a group, that owns, directly or indirectly, 50 percent or more of the total value or voting power of all outstanding stock of the Corporation; or (D) an entity, at least 50 percent of the total value or voting power of which is owned, directly or indirectly, by a person described in the previous subsection (C). For purposes of this paragraph, (1) gross fair market value means the value of the assets of the Corporation, or the value of the assets being disposed of, determined without regard to any liabilities associated with such assets, and (2) a person’s status is determined immediately after the transfer of the assets.

(d) any one person, or more than one person acting as a group, becomes owner, as defined in Section 318(a) of the Code, of stock of the Corporation that, together with stock held by such person or group, constitutes more than 50 percent of the total fair market value or total voting power of stock of the Corporation; provi