Second amendment, dated as of January 23, 2007, to the Amended and Restated 2002 Praxair, Inc. Long Term Incentive Plan

Exhibit 10.01b

AMENDMENT TO THE

RESTATED 2002 PRAXAIR, INC. LONG TERM INCENTIVE PLAN

The Restated 2002 Praxair, Inc. Long Term Incentive Plan (the “Plan”) is hereby amended as follows, effective as of January 23, 2007:

1. Section 6.7 of the Plan is hereby amended in its entirety as follows:

“6.7 Initial Vesting. A Stock Option Award by its terms shall be exercisable only after the earliest of:

(i) such period of time as the Committee shall determine and specify in the grant, but in no event less than three years following the date of grant of such award provided that options granted may partially vest after no less than one year so long as the entire grant does not fully vest until at least three years have elapsed from the date of grant;

(ii) the Participant’s death; or

(iii) a Change in Control of the Company.

In the event of the Participant’s Disability or Retirement or termination by the Company of the Participant’s employment other than for cause, a Stock Option Award shall not be exercisable at the time of such event but shall become exercisable at the time specified in clauses (i), (ii) or (iii) above. Notwithstanding the foregoing: (a) in the event of a Participant’s Retirement prior to the first anniversary date after the date of a Stock Option Award, such Stock Option Award shall not vest but shall be immediately forfeited; and (b) except as otherwise determined by the Company’s Chief Executive Officer or his designee, in the event of the termination by the Company of the Participant’s employment other than for cause prior to the first anniversary date after the date of a Stock Option Award, such Stock Option Award shall not vest but shall be immediately forfeited.”

2. Section 6.8(iii) is of the Plan is hereby amended in its entirety as follows:

“(iii) in the case of termination by the Company of the Participant’s employment other than for cause, the Stock Option Award, to the extent not forfeited in accordance with Section 6.7 above, shall remain exercisable during a three (3) year period commencing on the effective date of such termination;”