First Amendment, dated as of October 24, 2006, to the Amended and Restated 1995 Stock Option Plan for Non-Employee Directors

Exhibit 10.04a

AMENDMENT TO THE

PRAXAIR, INC. 1995 STOCK OPTION PLAN

FOR NON-EMPLOYEE DIRECTORS

Section 9 of the Praxair, Inc. 1995 Stock Option Plan for Non-Employee Directors is hereby amended in its entirety as follows, effective as of October 24, 2006:

“9. Dilution and Other Adjustment.

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 options then outstanding and in the number of shares which are available thereafter for option grants, both under the Plan as a whole and with respect to individuals. 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.”