AMENDMENT NO. 2 TO THE REDEEMABLE CLASS A WARRANT AGREEMENT

Exhibit 4.1

AMENDMENT NO. 2
TO THE
REDEEMABLE CLASS A
WARRANT AGREEMENT

     This Amendment No. 2 to the Warrant Agreement is dated as of June 6, 2002 by and between Hypertension Diagnostics, Inc., a Minnesota corporation (the “Company”), and U.S. Bank, N.A. (formerly known as Firstar Bank, N.A., formerly known as Firstar Trust Company), as Warrant Agent (the “Warrant Agent”).

     A.     The parties have entered into that certain Warrant Agreement dated as of July 23, 1998 (the “Class A Warrant Agreement”) which governs the rights and obligations of the Company and Warrant Agent with respect to up to 2,587,500 Redeemable Class A Warrants (each, a “Warrant”).

     B.     The parties amended the Class A Warrant Agreement by an Amendment No. 1 to Class A Warrant Agreement dated as of January 23, 2001 pursuant to which Section 2.1 of the Class A Warrant Agreement was amended to reduce the exercise price of the Warrants from $5.50 per share of Common Stock issuable upon exercise of the Warrant to $5.15 per share of Common Stock issuable upon exercise of the Warrant.

     C.     The Company desires (a) to extend the expiration date of the Class A Warrant set forth in Section 2.1 of the Class A Warrant Agreement from July 22, 2002 to August 7, 2002 and (b) to reduce the exercise price of the Warrants from $5.15 per share of Common Stock issuable upon exercise of the Warrant to $1.80 per share of Common Stock issuable upon exercise of the Warrant pursuant to Section 2.4 of the Class A Warrant Agreement.

     D.     The parties desire to set forth their mutual understanding in this Amendment No. 2 to the Class A Warrant Agreement.

     NOW, THEREFORE, in connection with and in consideration of the premises and the mutual agreements and covenants hereinafter set forth, the Company and Warrant Agent hereby agree as follows:

     1.     Capitalized terms used but not otherwise defined herein shall have the same meanings as in the Class A Warrant Agreement.

     2.     Section 2.1 of the Class A Warrant Agreement is hereby amended to read in its entirety as follows:

     Section 2.1 Exercise. Any or all of the Warrants represented by each Warrant Certificate may be exercised by the holder thereof on or before 5:00 p.m., Central Time, on August 7, 2002, unless extended by the Company, by surrender of the Warrant Certificate with the Purchase Form, which is printed on

the reverse thereof (or a reasonable facsimile thereof) duly executed by such holder, to the Warrant Agent at its principal office in Milwaukee, Wisconsin, accompanied by payment, in cash or by certified or official bank check payable to the order of the Company, in an amount equal to the product of the number of shares of Common Stock issuable upon exercise of the Warrant represented by such Warrant Certificate, as adjusted pursuant to the provisions of Article III hereof, multiplied by the exercise price of $1.80, as adjusted pursuant to the provisions of Article III hereof (such price as so adjusted from time to time being herein called the “Exercise Price”), and such holder shall be entitled to receive such number of fully paid and nonassessable shares of Common Stock, as so adjusted, at the time of such exercise.

     3.     The amendment to Section 2.1 as described in Paragraph 2 of this Amendment No. 2 to the Class A Warrant Agreement shall take effect as of the date the U.S. Securities and Exchange Commission declares effective the Company’s Registration Statement on Form S-3 filed April 5, 2002 (File No. 333-85632) and continue until the expiration of the Warrant on August 7, 2002, unless this expiration date shall be extended by the Company.

     4.     All other terms of the Class A Warrant Agreement shall remain in full force and effect until such time as they may be amended in writing by the parties.

     5.     This Amendment No. 2 to the Class A Warrant Agreement shall be construed and enforced in accordance with and governed by the laws of the State of Minnesota.

     IN WITNESS WHEREOF, the parties hereto have executed this Amendment No. 2 to the Class A Warrant Agreement as of the day and year first above written.

		HYPERTENSION DIAGNOSTICS, INC.
		By:		/s/ Xxxx X. Xxxxxxxx
				Its President
		U.S. BANK, N.A.
		By:		/s/ Xxxxxxx X. Xxxxxxxx
				Its Trust Officer

2