First amendment, dated as of October 24, 2006, to the Amended and Restated 2002 Praxair, Inc. Long Term Incentive Plan

Exhibit 10.01a

AMENDMENT TO THE

RESTATED 2002 PRAXAIR, INC. LONG TERM INCENTIVE PLAN

Section 5.3 of the Restated 2002 Praxair, Inc. Long Term Incentive Plan, is hereby amended in its entirety as follows, effective as of October 24, 2006:

“5.3 Adjustment in the Event of Recapitalization, etc. In the event of any change in the outstanding shares of the Company by reason of any stock split, stock dividend, recapitalization, merger, consolidation, combination or exchange of shares or other similar corporate change or in the event of any special distribution to the stockholders, the Committee shall make equitable adjustments in the number of shares and prices per share applicable to Stock Option Awards then outstanding and in the number of shares which are available thereafter for Stock Option Awards or other awards, both under the Plan as a whole and with respect to individuals and award type. Such adjustments shall be made in a manner that the Committee determines is necessary and appropriate, and shall be conclusive and binding for all purposes of the Plan.”