Virtu Itg 10-Q 2004 Q3 Quarterly report

Exhibit 32.1

Certification Under Section 906 of the Sarbanes-Oxley Act of 2002
(United States Code, Title 18, Chapter 63, Section 1350)
Accompanying Quarterly Report on Form 10-Q of
Investment Technology Group, Inc. for the Fiscal Quarter Ended September 30, 2004

In connection with the Quarterly Report on Form 10-Q of Investment Technology Group, Inc. (the “Company”) for the quarterly period ended September 30, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Raymond L. Killian, Jr., as Chief Executive Officer of the Company, and Howard C. Naphtali, as Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. (§)1350,  that:

(1)The Report fully complies with the requirements of Section 13(a) or 15(d), as applicable, 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 results of operations of the Company.

/s/ Raymond L. Killian, Jr.	/s/ Howard C. Naphtali
Raymond L. Killian, Jr.	Howard C. Naphtali
Chief Executive Officer	Chief Financial Officer
November 9, 2004	November 9, 2004

The foregoing certification is being furnished solely pursuant to 18 U.S.C. § 1350 and is not being filed as part of the Report or as a separate disclosure document.