Income Opportunity Realty Investors (IOR) 10-Q 2004 Q2 Quarterly report

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 Income Opportunity Realty Investors, Inc. (the “Company”), on Form 10-Q for the period ended June 30, 2004, as filed with Securities Exchange Commission on the date hereof (the “Report”), I, Ken L. Joines, Executive Vice President, Chief Financial Officer, and Acting Principal 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 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 Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

Date: August 15, 2004	/s/ Ken L. Joines
	Ken L. Joines
	Executive Vice President, Chief Financial Officer, and Acting Principal Executive Officer