Document:

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                                                                     Exhibit 4.1

                                 AMENDMENT NO. 3
                                     TO THE
                               REDEEMABLE CLASS A
                                WARRANT AGREEMENT

         This  Amendment  No. 3 to the Warrant  Agreement is dated as of July
25, 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 the 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: (a) 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; and (b) an Amendment No. 2 to Class A
Warrant Agreement dated as of June 6, 2002 pursuant to which Section 2.1 of the
Class A Warrant Agreement was amended 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
and to extend the expiration date of the Class A Warrant to August 7, 2002.
..
         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 August 7,
2002 to September 17, 2002 and (b) to reduce the exercise price of the Warrants
from $1.80 per share of Common Stock issuable upon exercise of the Warrant to
$1.25 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. 3 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
the 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:

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                  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 September 17, 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 $1.25, 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. 3 to the Class A Warrant Agreement shall take effect as of
the date hereof and continue until the expiration of the Warrant on September
17, 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. 3 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.
3 to the Class A Warrant Agreement as of the day and year first above written.

                                       HYPERTENSION DIAGNOSTICS, INC.

                                       By:  /s/ Greg H. Guettler
                                            ------------------------------------
                                            Its: President

                                       U.S. BANK, N.A.

                                       By:  /s/ Toula Akladios
                                            ------------------------------------
                                            Its: Vice President

                                       2<PAGE>

                                                                     Exhibit 4.2

                                 AMENDMENT NO. 3
                                     TO THE
                               REDEEMABLE CLASS B
                                WARRANT AGREEMENT

         This Amendment No. 3 to the Warrant Agreement is dated as of July 25,
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.), as
Warrant Agent (the "Warrant Agent").

         A. The parties have entered into that certain Warrant Agreement dated
as of January 4, 2001 (the "Class B Warrant Agreement") which governs the rights
and obligations of the Company and the Warrant Agent with respect to up to
2,752,192 Redeemable Class B Warrants (each, a "Warrant").

         B. The parties amended the Class B Warrant Agreement by: (a) an
Amendment No. 1 to Class B Warrant Agreement dated as of March 13, 2001 pursuant
to which Section 2.1 of the Class B Warrant Agreement was amended to reduce the
exercise price of the Warrants from $9.00 per share of Common Stock issuable
upon exercise of the Warrant to $5.85 per share of Common Stock issuable upon
exercise of the Warrant; and (b) an Amendment No. 2 to Class B Warrant Agreement
dated as of June 6, 2002 pursuant to which Section 2.1 of the Class B Warrant
Agreement was amended to reduce the exercise price of the Warrants from $5.85
per share of Common Stock issuable upon exercise of the Warrant to $2.00 per
share of Common Stock issuable upon exercise of the Warrant.

         C. The Company desires under Section 2.4 of the Class B Warrant
Agreement to reduce the exercise price of the Warrants from $2.00 per share of
Common Stock issuable upon exercise of the Warrant to $1.50 per share of Common
Stock issuable upon exercise of the Warrant.

         D. The parties desire to set forth their mutual understanding in this
Amendment No. 3 to the Class B 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
the Warrant Agent hereby agree as follows:

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

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

<PAGE>

         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 January 23, 2006, 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
         $1.50, 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. 3 to the Class B Warrant Agreement shall take effect as of
the date hereof and continue until the expiration of the Warrant on January 23,
2006, unless this expiration date shall be extended by the Company.

         4.       All other terms of the Class B 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. 3 to the Class B 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.
3 to the Class B Warrant Agreement as of the day and year first above written.

                                       HYPERTENSION DIAGNOSTICS, INC.

                                       By: /s/ Greg H. Guettler
                                           -------------------------------------
                                           Its:  President

                                       U.S. BANK, N.A.

                                       By: /s/ Toula Akladios
                                           -------------------------------------
                                           Its:  Vice President

                                       2

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