Exhibit 32.1

CERTIFICATION BY CHIEF EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Rockwell Collins, Inc. (the “Company”) on Form 10-Q for the quarter ended June 30, 2004 (the “Report”) filed with the Securities and Exchange Commission, I, Clayton M. Jones, Chairman, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Company’s Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: August 3, 2004	/s/ Clayton M. Jones
	Clayton M. Jones
	Chairman, President and
	Chief Executive Officer