First Amendment, dated as of October 24, 2006, to the 2005 Equity Compensation Plan for Non-Employee Directors of Praxair, Inc

Exhibit 10.04c

FIRST AMENDMENT TO THE

2005 EQUITY COMPENSATION PLAN

FOR NON-EMPLOYEE DIRECTORS OF PRAXAIR, INC.

Section 5.10 of the 2005 Equity Compensation Plan for Non-Employee Directors of Praxair, Inc., is hereby amended in its entirety as follows, effective as of October 24, 2006:

“5.10 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 grants then outstanding and in the number of shares which are available thereafter for Stock Option grants 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.”