EXHIBIT 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in this Registration Statement of Reliance Bancorp, Inc. on Form S-4 of our report dated July 24, 1997, incorporated by reference in the Annual Report on Form 10-K of Reliance Bancorp, Inc. for the year ended June 30, 1997 and to the reference to our firm the heading "Experts" in the Prospectus, which is part of this Registration Statement. /s/ KPMG PEAT MARWICK LLP - --------------------------- Melville, New York September 24, 1998 A-1