Exhibit 32.1

CERTIFICATION 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 The Home Depot, Inc. (the “Company”) on Form 10-Q (“Form 10-Q”) for the period ended July 31, 2005 as filed with the Securities and Exchange Commission on the date hereof, I, Robert L. Nardelli, 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, to my knowledge:

(1)The Form 10-Q 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.

/s/ ROBERT L. NARDELLI

Robert L. Nardelli

Chairman, President and

Chief Executive Officer

August 31, 2005

*A signed original of this written statement required by Section 906 has been provided to The Home Depot, Inc. and will be retained by The Home Depot, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.