First amendment to the Praxair, Inc. Supplemental Retirement Income Plan A effective January 1, 2010 is

Exhibit 10.05b

FIRST AMENDMENT TO THE

PRAXAIR, INC.

SUPPLEMENTAL RETIREMENT INCOME PLAN A

(EFFECTIVE JANUARY 1, 2008)

Article III, Section 1(c) of the Praxair, Inc. Supplemental Retirement Income Plan A (Effective January 1, 2008) is hereby amended by the addition of the following sentence at the end thereof, effective as of January 1, 2010:

“Notwithstanding the prior sentence, with respect to benefits that become payable on account of a Traditional-Design Participant’s termination of employment occurring after December 31, 2009, lump sum payments shall be calculated using a discount rate equal to the average of the 10 year Aaa municipal bond rate as published by Moody’s or a similar rating service for the months of July through December of the year immediately prior to the year in which such Participant terminated employment.”