<PAGE>   1
                                                                     EXHIBIT 4.5

                                WARRANT AGREEMENT


         WARRANT AGREEMENT dated as of January 4, 2001 by and between
Hypertension Diagnostics, Inc., a Minnesota corporation (the "Company"), and
Firstar Bank N.A., as Warrant Agent (the "Warrant Agent").

         A. The Company proposes to issue up to 2,752,192 Redeemable Class B
Warrants (the "Warrants") evidencing the right to purchase an aggregate of up to
2,752,192 authorized but previously unissued shares of Common Stock, $.01 par
value per share, of the Company (the "Common Stock"). The Warrants would be
issued in connection with the proper exercise by the Redeemable Class A Warrant
holders of their Redeemable Class A Warrant during the term of the offering as
defined by the Company's Registration Statement on Form S-3 (File No.
333-53200), filed with the Securities and Exchange Commission on January 4, 2001
and as subsequently amended.

         B. The Company desires the Warrant Agent to act on behalf of the
Company, and the Warrant Agent desires so to act, in connection with the
issuance, registration, transfer, exchange and exercise of the Warrants.

         NOW THEREFORE, it is agreed as follows:


                                   ARTICLE 1.
                     APPOINTMENT OF WARRANT AGENT; ISSUANCE,
                   FORM AND EXECUTION OF WARRANT CERTIFICATES


         Section 1.1 Appointment of Warrant Agent. The Company hereby appoints
the Warrant Agent to act as agent for the Company, and the Warrant Agent hereby
accepts the agency established herein and agrees to perform its agency duties in
accordance with the terms and conditions of this Warrant Agreement.



         Section 1.2 Warrant Certificates. The Company shall execute and deliver
to the Warrant Agent certificates which the Company has authorized to represent
the Warrants ("Warrant Certificates"). The Warrant Certificates shall be
substantially as set forth in Exhibit A hereto and may have such legends,
summaries or endorsements printed, lithographed or engraved thereon as the
Company may deem appropriate and as are not inconsistent with the provisions of
this Warrant Agreement, or as may be required to comply with any law or with any
rule or regulation relating to listing of the Warrants on The Nasdaq Stock
Market ("Nasdaq"), including the SmallCap Market, or on any stock exchange or to
conform to usage. The Warrant Certificates shall be dated with the date of their
issuance.




<PAGE>   2




         Section 1.3 Execution of Warrant Certificates. The Warrant Certificates
shall be executed on behalf of the Company by a duly authorized officer of the
Company, either manually or by facsimile signature printed thereon. The Warrant
Certificates shall be manually countersigned by the Warrant Agent and shall not
be valid for any purpose unless so countersigned. Any Warrant Certificate may be
signed on behalf of the Company by the person who at the actual date of the
signing of such Warrant Certificate shall have been the proper officer of the
Company, although at the date of issuance of such Warrant Certificate any such
person has ceased to be such officer of the Company.


                                   ARTICLE II.
                              EXERCISE OF WARRANTS

         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., Minneapolis 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 $9.00, 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.


         Section 2.2 Time of Exercise. Each exercise of Warrants shall be deemed
to have been effective immediately prior to the close of business on the
business day on which the Warrant Certificate relating to such Warrants shall
have been surrendered to the Warrant Agent as provided in Section 2.1, and at
such time the person or persons in whose name or names any certificate or
certificates for shares of Common Stock shall be issuable upon such exercise as
provided in Section 2.3, shall be deemed to have become the holder or holders of
record thereof.


         Section 2.3 Issuance of Shares of Common Stock; No Fractional Shares.
As soon as practicable after the exercise of any Warrant, and in any event
within ten (10) days after receipt by the Warrant Agent of the notice of
exercise under Section 2.1, the Company at its expense (including the payment by
it of any applicable issue taxes) will cause to be issued in the name of and
delivered to the holder thereof or as such holder (upon payment by such holder
of any applicable transfer taxes) may direct,

                  (a) certificate or certificates for the number of fully paid
         and nonassessable shares of Common Stock to which such holder shall be
         entitled upon such exercise plus, in lieu of any fractional share to
         which such holder would otherwise be entitled, an





                                       2
<PAGE>   3


         amount in cash equal to such fraction multiplied by the then current
         value of a share of Common Stock, determined as follows:

                           (i) if the Common Stock is listed or admitted to
                  unlisted trading privileges on any single stock exchange, then
                  such current value shall be computed on the basis of the last
                  reported sale price of the Common Stock on such exchange on
                  the last business day prior to the date of the exercise of
                  such Warrant upon which a sale shall have been effected; or


                           (ii) if the Common Stock is not so listed or admitted
                  to unlisted trading privileges and bid and ask prices are
                  reported by Nasdaq, including the SmallCap Market system (or,
                  if not so quoted on Nasdaq, by the National Quotation Bureau,
                  Inc.), then the current value shall be the last reported sale
                  on the last business day prior to the date of the exercise of
                  such Warrant, or, in the event the last reported sale is
                  unavailable, the average of the closing bid and ask prices
                  on the last business day prior to the date of the exercise of
                  such Warrant as so reported; or


                           (iii) if the Common Stock is listed or admitted to
                  unlisted trading privileges on more than one stock exchange or
                  one or more stock exchanges and quoted on Nasdaq, then the
                  current value shall, if different as a result of calculation
                  under the applicable method(s) described above in this
                  Section, be deemed to be the higher number calculated in
                  connection therewith; or


                           (iv) if the Common Stock is not so listed or admitted
                  to unlisted trading privileges and bid and ask prices are
                  not so reported, then the current value shall be computed on
                  the basis of the book value of Common Stock as of the close of
                  business on the last day of the month immediately preceding
                  the date upon which such Warrant was exercised, as determined
                  by the Company,


                  and

                  (b) in case such exercise includes only part of the Warrants
         represented by any Warrant Certificate, a new Warrant Certificate or
         Warrant Certificates of like tenor, calling in the aggregate on the
         face or faces thereof for the number of shares of Common Stock equal
         (without giving effect to any adjustment therein) to the number of such
         shares called for on the face of such Warrant Certificate minus the
         number of such shares designated by the holder for such exercise as
         provided in Section 2.1. Warrants, represented by a properly assigned
         Warrant Certificate, may be exercised by a new holder without first
         having a new Warrant Certificate issued.

         Section 2.4 Extension of Exercise Period; Change of Exercise Price. The
Company may, upon notice given to the Warrant Agent, and without the consent of
the holders of the Warrant Certificates, (i) reduce the Exercise Price during
all or any portion of the originally stated exercise period, or (ii) extend the
period over which the Warrants are exercisable beyond





                                       3
<PAGE>   4



January 23, 2006 and increase the Exercise Price for any period the Warrant
exercise period is extended. In the case of the extension of the exercise period
or a change in the Exercise Price, the Company must provide the Warrant Agent
and the Warrant holders of record notice of such extension of the exercise
period, specifying, as the case may be, the time to which such exercise period
is extended, or specifying the new Exercise Price and the periods for which such
new Exercise Price is in effect, a reasonable time prior to the date such
extension or new Exercise Price is to take effect, such reasonable time to be
commercially reasonable and consistent with applicable securities laws and
regulations.



                                  ARTICLE III.
                             ANTIDILUTION PROVISIONS

         Section 3.1 Adjustment of Exercise Price.

                  (a) The Exercise Price shall be subject to the following
         adjustments. In the event that:


                           (i) any dividends on any class of stock of the
                  Company payable in Common Stock or securities convertible into
                  Common Stock shall be paid by the Company; or


                           (ii) the Company shall subdivide its then outstanding
                  shares of Common Stock into a greater number of shares; or

                           (iii) the Company shall combine outstanding shares of
                  Common Stock, by reclassification or otherwise;

         then, in any such event, the Exercise Price in effect immediately prior
         to such event shall (until adjusted again pursuant hereto) be adjusted
         immediately after such event to a price (calculated to the nearest full
         cent) determined by dividing (A) the number of shares of Common Stock
         outstanding immediately prior to such event, multiplied by the then
         existing Exercise Price, by (B) the total number of shares of Common
         Stock outstanding immediately after such event (including the maximum
         number of shares of Common Stock issuable in respect of any securities
         convertible into Common Stock), and the resulting quotient shall be the
         adjusted Exercise Price per share.

                  (b) No adjustment of the Exercise Price shall be made if the
         amount of such adjustments shall be less than one cent per share, but
         in such case any adjustment that would otherwise be required to be made
         shall be carried forward and shall be made at the time and together
         with the next subsequent adjustment which, together with any adjustment
         or adjustments so carried forward, shall amount to not less than one
         cent per share.




                                       4
<PAGE>   5


         Section 3.2 Adjustment of Number of Shares Purchasable on Exercise of
Warrants. Upon each adjustment of the Exercise Price pursuant to Section 3.1,
the registered holder of each Warrant shall thereafter (until another such
adjustment) be entitled to purchase at the adjusted Exercise Price the number of
shares, calculated to the nearest full share, obtained by multiplying the number
of shares specified in such Warrant (as adjusted as a result of all adjustments
in the Exercise Price in effect prior to such adjustment) by the Exercise Price
in effect prior to such adjustment and dividing the product so obtained by the
adjusted Exercise Price.


         Section 3.3 Notice as to Adjustment. Upon any adjustment of the
Exercise Price and an increase or decrease in the number of shares of Common
Stock purchasable upon the exercise of the Warrants, then, and in each such
case, the Company shall within ten (10) days after the effective date of such
adjustment give written notice thereof, by first class mail, postage prepaid,
addressed to each registered Warrant holder at the address of such Warrant
holder as shown on the books of the Company, which notice shall state the
adjusted Exercise Price and the increased or decreased number of shares
purchasable upon the exercise of the Warrants, setting forth in reasonable
detail the method of calculation and the facts upon which such calculation is
based.



         Section 3.4 Effect of Reorganization, Reclassification, Merger, Etc. If
at any time while any Warrant is outstanding there should be any capital
reorganization or reclassification of the capital stock of the Company (other
than the issue of any shares of Common Stock in subdivision of outstanding
shares of Common Stock by reclassification or otherwise and other than a
combination of shares provided for in Section 3.1 hereof) or any consolidation
or merger of the Company with another corporation or any sale, conveyance, lease
or other transfer by the Company of all or substantially all of its assets to
any other corporation, the holder of any Warrant shall, during the remainder of
the period such Warrant is exercisable, be entitled to receive, upon payment of
the Exercise Price, the number of shares of stock or other securities or
property of the Company, or of the successor corporation resulting from such
consolidation or merger, or of the corporation to which the assets of the
Company has been sold, conveyed, leased or otherwise transferred, as the case
may be, to which the Common Stock (and any other securities and property) of the
Company, deliverable upon the exercise of such Warrant, would have been entitled
upon such capital reorganization, reclassification of capital stock,
consolidation, merger, sale, conveyance, lease or other transfer if such Warrant
had been exercised immediately prior to such capital reorganization,
reclassification of capital stock, consolidation merger, sale, conveyance, lease
or other transfer; and, in any such case, appropriate adjustment (as determined
by the Board of Directors of the Company) shall be made in the application of
the provisions set forth in this Warrant Agreement with respect to the rights
and interests thereafter of the Warrant holders to the end that the provisions
set forth in this Warrant Agreement (including the adjustment of the Exercise
Price and the number of shares issuable upon the exercise of the Warrants) shall
thereafter be applicable, as near as may be reasonably practicable, in relation
to any shares or other property thereafter deliverable upon the exercise of the
Warrants as if the Warrants had been exercised immediately prior to such capital
reorganization, reclassification of capital stock, such consolidation, merger,
sale, conveyance, lease or other transfer and the Warrant holders had carried
out the terms of the exchange as provided for by such capital reorganization,
reclassification, consolidation or merger. The Company shall not effect any such
capital reorganization, consolidation, merger or transfer






                                       5
<PAGE>   6

unless, upon or prior to the consummation thereof, the successor corporation or
the corporation to which the property of the Company has been sold, conveyed,
leased or otherwise transferred shall assume by written instrument the
obligation to deliver to the holder of each Warrant such shares of stock,
securities, cash or property as in accordance with the foregoing provisions such
holder shall be entitled to purchase.

         Section 3.5 Prior Notice as to Certain Events. In case at any time:

                  (a) The Company shall pay any dividend upon its Common Stock
         payable in stock or make any distribution (other than cash dividends)
         to the holders of its Common Stock; or

                  (b) The Company shall offer for subscription pro rata to the
         holders of its Common Stock any additional shares of stock of any class
         or any other rights; or

                  (c) There shall be any capital reorganization or
         reclassification of the capital stock of the Company, or consolidation
         or merger of the Company with, or sale, conveyance, lease or other
         transfer of all or substantially all of its assets to, another
         corporation; or

                  (d) There shall be a voluntary or involuntary dissolution,
         liquidation or winding up of the Company;


then in any one or more of such cases, the Company shall give prior written
notice, by first class mail, postage prepaid, addressed to each registered
Warrant holder at the address of such Warrant holder as shown on the books of
the Company, of the date on which (i) the books of the Company shall close or a
record shall be taken for such stock dividend, distribution or subscription
rights or (ii) such reorganization, reclassification, consolidation, merger,
sale, dissolution, liquidation or winding up shall take place, as the case may
be. Such notice shall also specify the date as of which the holders of the
Common Stock of record shall participate in such dividend, distribution or
subscription rights or shall be entitled to exchange their Common Stock for
securities or other property deliverable upon such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation, or
winding up, as the case may be. Such written notice shall be given at least
twenty (20) days prior to the action in question and not less than twenty (20)
days prior to the record date or the date on which the Company's transfer books
are closed in respect thereto.


         Section 3.6 Certain Obligations of the Company. The Company will not,
by amendment of its articles of incorporation or through any reorganization,
transfer of assets, consolidation, merger, dissolution, issue or sale of
securities or any other voluntary action, avoid or seek to avoid the observance
or performance of any of the terms of this Warrant Agreement or the Warrant
Certificate, but will at all times in good faith assist in the carrying out of
all such terms. Without limiting the generality of the foregoing, the Company
(a) will take all such action as may be necessary or appropriate in order that
the Company may validly and legally issue fully paid and nonassessable shares of
such stock upon the exercise of all Warrants from





                                       6
<PAGE>   7

time to time outstanding, and (b) will not (i) transfer all or substantially all
of its properties and assets to any other person or entity, or (ii) consolidate
with or merge into any other entity where the Company is not the continuing or
surviving entity, or (iii) permit any other entity to consolidate with or merge
into the Company where the Company is the continuing or surviving entity but, in
connection with such consolidation or merger, the Common Stock then issuable
upon the exercise of the Warrants shall be changed into or exchanged for shares
or other securities or property of any other entity unless, in any such case,
the other entity acquiring such properties and assets, continuing or surviving
after such consolidation or merger or issuing or distributing such shares or
other securities or property, as the case may be, shall expressly assume in
writing and be bound by all the terms of this Warrant Agreement and the Warrant
Certificates.


         Section 3.7 Reservation and Listing of Common Stock. The Company will
at all times reserve and keep available, solely for issuance and delivery upon
the exercise of the Warrants, all shares of Common Stock from time to time
issuable upon such exercise. All such shares shall be duly and validly issued,
fully paid and nonassessable with no liability on the part of the holder
thereof. The Company, at its expense, will list on The Nasdaq SmallCap Market
(subject to official notice of issuance) and will maintain such listing of, the
shares of Common Stock from time to time issuable upon the exercise of the
Warrants.


         Section 3.8 Registration or Exemption of Common Stock. The Company will
use its best efforts (a) at all times the Warrants are exercisable to maintain
an effective registration statement under the Securities Act of 1933, as amended
(the "Act"), covering Common Stock issuable upon exercise of the Warrants, (b)
from time to time to amend or supplement the prospectus contained in such
registration statement to the extent necessary in order to comply with
applicable law, (c) to qualify for exemption from the registration requirements
of the Act the Common Stock issuable upon exercise of the Warrants, and (d) to
maintain exemptions or qualifications, in those jurisdictions in which the
original registration statement relating to the Warrants was initially
qualified, to permit the exercise of the Warrants and the issuance of the Common
Stock pursuant to such exercise. The Warrant Agent shall have no responsibility
for the maintenance of such exemptions or qualifications or for liabilities
arising from the exercise or attempted exercise of Warrants in jurisdictions
where exemptions or qualifications have not been maintained or are otherwise
unavailable.


                                   ARTICLE IV.
                              REDEMPTION OF WARRANT


         Section 4.1 Redemption Price. The Warrants may be redeemed at the
option of the Company, anytime following a period of five (5) consecutive
trading days where the per share closing bid price of the Common Stock exceeds
$13.50, on notice as set forth in Section 4.2, and at a redemption price equal
to $.01 per Warrant. For purposes of this Section, the closing bid price of the
Common Stock shall be determined by the closing bid price as reported by The
Nasdaq SmallCap Market so long as the Common Stock is quoted on The Nasdaq
SmallCap Market and, if the







                                       7
<PAGE>   8

Common Stock is listed on a stock exchange, shall be determined by the last
reported sale price on the primary exchange on which the Common Stock is traded.

         Section 4.2 Notice of Redemption. In the case of any redemption of
Warrants, the Company or, at its request, the Warrant Agent in the name of and
at the expense of the Company shall give notice of such redemption to the
holders of the Warrants to be redeemed as hereinafter provided in this Section
4.2. Notice of redemption to the holders of Warrants shall be given by mailing
by first-class mail a notice of such redemption at any time following the
five-day consecutive trading period referenced in Section 4.1 and not less than
30 days prior to the date fixed for redemption. Any notice which is given in the
manner herein provided shall be conclusively presumed to have been duly given,
whether or not the holder receives the notice. In any case, failure duly to give
such notice, or any defect in such notice, to the holder of any Warrant
Certificate shall not affect the validity of the proceedings for the redemption
of Warrants represented by any other Warrant Certificate. Each such notice shall
specify the date fixed for redemption, the place of redemption and the
redemption price of $.01 at which each Warrant is to be redeemed, and shall
state that payment of the redemption price of the Warrants will be made on
surrender of the Warrants at such place of redemption, and that if not exercised
by the close of business on the date fixed for redemption the exercise rights of
the Warrants identified for redemption shall expire unless extended by the
Company. Such notice shall also state the current Exercise Price and the date on
which the right to exercise the Warrants will expire unless extended by the
Company.

         Section 4.3 Payment of Warrants on Redemption; Deposit of Redemption
Price. If notice of redemption shall have been given as provided in Section 4.2,
the redemption price of $.01 per Warrant shall, unless the Warrant is
theretofore exercised pursuant to the terms hereof, become due and payable on
the date and at the place stated in such notice. On and after such date of
redemption, provided that cash sufficient for the redemption thereof shall then
be deposited by the Company with the Warrant Agent for that purpose, the
exercise rights of the Warrants identified for redemption shall expire. On
presentation and surrender of Warrant Certificates at such place of payment in
such notice specified, the Warrants identified for redemption shall be paid and
redeemed at the redemption price of $.01 per Warrant. Prior to the date fixed
for redemption, the Company shall deposit with the Warrant Agent an amount of
money sufficient to pay the redemption price of all the Warrants identified for
redemption. Any monies which shall have been deposited with the Warrant Agent
for redemption of Warrants and which are not required for that purpose by reason
of exercise of Warrants shall be repaid to the Company upon delivery to the
Warrant Agent of evidence satisfactory to it of such exercise.


                                   ARTICLE V.
                      CERTAIN OTHER PROVISIONS RELATING TO
                    RIGHTS OF HOLDERS OF WARRANT CERTIFICATES

         Section 5.1 No Rights of Shareholders. The Warrant Certificates shall
be issued in registered form only. No Warrant Certificate shall entitle the
holder thereof to any of the rights of a holder of shares of Common Stock of the
Company, including, without limitation, the right




                                       8
<PAGE>   9

to vote, to receive dividends and other distributions, or to receive any notice
of, or to attend, meetings of holders of Common Stock or any other proceedings
of the Company.

         Section 5.2 Loss, Theft, Destruction or Mutilation of Warrant
Certificates. Upon receipt by the Warrant Agent of evidence reasonably
satisfactory to the Warrant Agent of the loss, theft, destruction or mutilation
of any Warrant Certificate, and (a) in the case of any such loss, theft, or
destruction, upon delivery to the Warrant Agent of an indemnity bond in form and
amount, and issued by a bonding company, reasonably satisfactory to the Company,
or (b) in the case of any such mutilation upon surrender to and cancellation by
the Warrant Agent of such Warrant Certificate, the Company at its expense will
execute and cause the Warrant Agent to countersign and deliver, in lieu thereof,
a new Warrant Certificate of like tenor.

         Section 5.3 Transfer Agent; Cancellation of Warrant Certificates;
Unexercised Warrants. Firstar Bank, N.A. (and any successor), as transfer agent
(the "Transfer Agent"), is hereby irrevocably authorized and directed at all
times to reserve such number of authorized and unissued shares of Common Stock
as shall be sufficient to permit the exercise in full of all Warrants from time
to time outstanding. The Company will keep a copy of this Agreement on file with
the Transfer Agent. The Warrant Agent, and any successor thereto, is hereby
irrevocably authorized to requisition from time to time from the Transfer Agent
certificates for shares of Common Stock required for exercise of Warrants. The
Company will supply the Transfer Agent with duly executed certificates for
shares of Common Stock for such purpose and will make available any cash
required in settlement of fractional share interests. All Warrant Certificates
surrendered upon the exercise or redemption of Warrants shall be canceled by the
Warrant Agent and shall thereafter be delivered to the Company; such canceled
Warrant Certificates, with the Purchase Form on the reverse thereof duly filled
in and signed, shall constitute conclusive evidence as between the parties
hereto of the numbers of shares of Common Stock which shall have been issued
upon exercises of Warrants. Promptly after the last day on which the Warrants
are exercisable (set forth in Section 2.1 above), the Warrant Agent shall
certify to the Company the aggregate number of Warrants then outstanding and
unexercised. No shares of Common Stock shall be subject to reservation with
respect to Warrants not exercised prior to the time and date identified in
Section 2.1 above as the last time and date at which Warrants may be exercised.


                                   ARTICLE VI.
                  TRANSFER AND EXCHANGE OF WARRANT CERTIFICATES

         Section 6.1 Warrant Register; Transfer or Exchange of Warrant
Certificates. The Warrant Agent shall cause to be kept at the principal office
of the Warrant Agent a register (the "Warrant Register") in which, subject to
such reasonable regulations as the Company may prescribe, provisions shall be
made for the registration of transfers and exchanges of Warrant Certificates.
Upon surrender for transfer or exchange of any Warrant Certificates, properly
endorsed, to the Warrant Agent, the Warrant Agent at the Company's expense will
issue and deliver to or upon the order of the holder thereof a new Warrant
Certificate or Warrant Certificates of like tenor, in the name of such holder or
as such holder (upon payment by such








                                       9
<PAGE>   10

holder of any applicable transfer taxes) may direct, calling in the aggregate on
the face or faces thereof for the number of shares of Common Stock called for on
the face of the Warrant Certificate so surrendered. Any Warrant Certificate
surrendered for transfer or exchange shall be canceled by the Warrant Agent and
shall thereafter be delivered to the Company.


         Section 6.2 Identity of Warrant holders. Until a Warrant Certificate is
transferred in the Warrant Register, the Company and the Warrant Agent may treat
the person in whose name the Warrant Certificate is registered as the absolute
owner thereof and of the Warrants represented thereby for all purposes,
notwithstanding any notice to the contrary, except that, if and when any Warrant
Certificate is properly assigned in blank, the Company and the Warrant Agent may
(but shall not be obligated to) treat the bearer thereof as the absolute owner
of the Warrant Certificate and of the Warrants represented thereby for all
purposes, notwithstanding any notice to the contrary.



                                  ARTICLE VII.
                          CONCERNING THE WARRANT AGENT

         Section 7.1 Taxes. The Company will, from time to time, promptly pay to
the Warrant Agent, or make provision satisfactory to the Warrant Agent for the
payment of, all taxes and charges that may be imposed by the United States or
any State upon the Company or the Warrant Agent upon the transfer or delivery of
shares of Common Stock upon the exercise of Warrants, but the Company shall not
be obligated to pay any tax imposed in connection with any transfer involved in
the delivery of a certificate for shares of Common Stock in any name other than
that of the registered holder of the Warrant Certificate surrendered in
connection with the purchase thereof.

         Section 7.2 Replacement of Warrant Agent in Certain Circumstances.


                  (a) The Warrant Agent may resign its duties and be discharged
         from all further duties and liabilities hereunder after giving thirty
         (30) days' notice in writing to the Company, except that such shorter
         notice may be given as the Company shall, in writing, accept as
         sufficient. The Company may discharge the Warrant Agent at any time
         with or without reason, effective upon thirty (30) days written notice
         to the Warrant Agent or such shorter period as the Warrant Agent shall,
         in writing, accept as sufficient. If the office of Warrant Agent
         becomes vacant by resignation, discharge, incapacity to act or
         otherwise, the Company shall appoint in writing a new Warrant Agent,
         the principal office of which shall be in Minnesota. If the Company
         shall fail to make such appointment within a period of thirty (30) days
         after it has been notified in writing of such resignation or incapacity
         by the resigning or incapacitated Warrant Agent or by the holder of a
         Warrant Certificate, then the holder of any Warrant Certificate may
         apply to any court of competent jurisdiction for the appointment of a
         new Warrant Agent. Any new Warrant Agent, whether appointed by the
         Company or by such a court, shall be a corporation organized and doing
         business under the laws of the United States and of the State of
         Minnesota, of good standing, and having its principal office in
         Minnesota, which






                                       10
<PAGE>   11


         is authorized under such laws to exercise corporate trust powers and is
         subject to supervision or examination by Federal or State authority.
         Any new Warrant Agent appointed hereunder shall execute, acknowledge
         and deliver to the Company an instrument accepting such appointment
         hereunder and thereupon such new Warrant Agent without any further act
         or deed shall become vested with all the rights, powers, duties and
         responsibilities of the Warrant Agent hereunder with like effect as if
         it had been named as the Warrant Agent; but if for any reason it
         becomes necessary or expedient to have the former Warrant Agent execute
         and deliver any further assurance, conveyance, act or deed, the same
         shall be done and shall be legally and validly executed and delivered
         by the former Warrant Agent. Not later than the effective date of any
         such appointment, the Company shall file notice thereof with the former
         Warrant Agent. The Company shall promptly give notice of any such
         appointment to the holders of the Warrant Certificates by mail to their
         addresses as shown in the Warrant Register. Failure to file or give
         such notice, or any defect therein, shall not affect the legality or
         validity of the appointment of the successor Warrant Agent.



                  (b) Any company into which the Warrant Agent or any new
         Warrant Agent may be merged or converted or with which it may be
         consolidated or any company resulting from any merger, conversion or
         consolidation to which the Warrant Agent shall be a party shall be the
         successor Warrant Agent under this Warrant Agreement without any
         further act; provided that if such company would not be eligible for
         appointment as a successor Warrant Agent under the provisions of
         paragraph (a) of this Section 7.2, the Company shall forthwith appoint
         a new Warrant Agent in accordance with such provisions. Any such
         successor Warrant Agent may adopt the prior countersignature of any
         predecessor Warrant Agent and deliver Warrant Certificates
         countersigned and not delivered by such predecessor Warrant Agent or
         may countersign Warrant Certificates either in the name of any
         predecessor Warrant Agent or the name of the successor Warrant Agent.


         Section 7.3 Remuneration of Warrant Agent. The Company will pay the
Warrant Agent reasonable remuneration for its services as Warrant Agent
hereunder and will reimburse the Warrant Agent upon demand for all expenditures
that the Warrant Agent may reasonably incur in the execution of its duties
hereunder.

         Section 7.4 Further Assurances. The Company will perform, exercise,
acknowledge and deliver or cause to be performed, executed, acknowledged and
delivered all such further and other acts, instruments and assurances as may
reasonably be required by the Warrant Agent for the carrying out or performing
by the Warrant Agent of the provisions of this Warrant Agreement.

         Section 7.5 Limitations on Liabilities of the Warrant Agent.

                  (a) The Warrant Agent may consult with legal counsel (who may
         be legal counsel for the Company), and the opinion of such counsel
         shall be full and complete






                                       11
<PAGE>   12

         authorization and protection of the Warrant Agent as to any action
         taken or omitted by it in good faith and in accordance with such
         opinion.

                  (b) Whenever, in the performance of its duties under this
         Warrant Agreement, the Warrant Agent shall deem it necessary or
         desirable that any matter be proved or established, or that any
         instructions with respect to the performance of its duties hereunder be
         given, by the Company prior to taking or suffering any action
         hereunder, such matter (unless other evidence in respect thereof be
         herein specifically prescribed) may be deemed to be conclusively proved
         and established, or such instructions may be given, by a certificate or
         instrument signed by an officer of the Company and delivered to the
         Warrant Agent; and such certificate or instrument shall be full
         authorization to the Warrant Agent for any action taken or suffered in
         good faith by it under the provisions of this Warrant Agreement in
         reliance upon such certificate or instrument; but in its discretion the
         Warrant Agent may in lieu thereof accept other evidence of such matter
         or may require such further or additional evidence as it may deem
         reasonable.

                  (c) The Warrant Agent shall be liable hereunder only for its
         own negligence or willful misconduct. The Warrant Agent shall act
         hereunder solely as agent, and its duties shall be determined solely by
         the provisions hereof. The Company agrees to indemnify the Warrant
         Agent and save it harmless against any and all liabilities, including
         judgments, costs and counsel fees, for anything done or omitted by the
         Warrant Agent in the execution of this Warrant Agreement except as a
         result of the Warrant Agent's negligence or willful misconduct.

                  (d) The Warrant Agent shall not be liable for or by reason of
         any of the statements of fact or recitals contained in this Warrant
         Agreement or in the Warrant Certificates (except its countersignature
         thereof) or be required to verify the same, but all such statements and
         recitals are and shall be deemed to have been made by the Company only.

                  (e) The Warrant Agent shall not be under any responsibility in
         respect to the validity or execution of any Warrant Certificate (except
         its countersignature thereof); nor shall it be responsible for any
         breach by the Company of any covenant or condition contained in this
         Warrant Agreement or in any Warrant Certificate; nor shall it be
         responsible for the making of any adjustment in the Exercise Price, or
         number of shares issuable upon exercise of the Warrant Certificates or
         responsible for the manner, method or amount of any such adjustment or
         the facts that would require any such adjustment; nor shall it by any
         act hereunder be deemed to make any representation or warranty as to
         the authorization or reservation of any shares of Common Stock to be
         issued pursuant to this Warrant Agreement or any Warrant Certificate or
         as to whether any shares of Common Stock or other securities are or
         will be validly authorized and issued and fully paid and nonassessable.

         Section 7.6 Amendment and Modification. The Warrant Agent may, without
the consent or concurrence of the holders of the Warrant Certificates, by
supplemental agreement or





                                       12
<PAGE>   13

otherwise, join with the Company in making any changes or corrections in this
Warrant Agreement that they shall have been advised by counsel (a) are required
to cure any ambiguity or to correct any defective or inconsistent provision or
clerical omission or mistake or manifest error herein contained, (b) add to the
obligations of the Company in this Warrant Agreement further obligations
thereafter to be observed by it, or surrender any right or power reserved to or
conferred upon the Company in this Warrant Agreement, or (c) do not or will not
adversely affect, alter or change the rights, privileges or immunities of the
holders of Warrant Certificates not provided for under this Warrant Agreement;
provided, however, that any term of this Warrant Agreement or any Warrant
Certificate may be changed, waived, discharged or terminated by an instrument in
writing signed by each party against which enforcement of such change, waiver,
discharge or termination is sought, or by which the same is to be performed or
observed.


                                  ARTICLE VIII.
                                  OTHER MATTERS

         Section 8.1 Successors and Assigns. All the covenants and provisions of
this Warrant Agreement by or for the benefit of the Company or the Warrant Agent
shall bind and inure to the benefit of their respective successors and assigns.

         Section 8.2 Notices. Any notice or demand authorized by this Warrant
Agreement to be given or made by the Warrant Agent or by the holder of any
Warrant Certificate to or on the Company shall be sufficiently given or made if
sent by first class or registered mail, postage prepaid, addressed (until
another address is filed in writing by the Company with the Warrant Agent) as
follows:

                  Attn:  President
                  Hypertension Diagnostics, Inc.
                  2915 Waters Road, Suite 108
                  Eagan, MN 55121-1562

                  With a copy to:

                  Girard P. Miller, Esq.
                  Lindquist & Vennum P.L.L.P.
                  4200 IDS Center
                  80 South Eighth Street
                  Minneapolis, MN 55402-2205

Any notice or demand authorized by this Warrant Agreement to be given or made by
the holder of any Warrant Certificate or by the Company to or on the Warrant
Agent shall be sufficiently given or made if sent by first class or registered
mail, postage prepaid, addressed (until another address is filed in writing by
the Warrant Agent with the Company) as follows:




                                       13
<PAGE>   14



                  Firstar Bank, N.A.
                  1555 N. RiverCenter Drive, Suite 301
                  Milwaukee, WI 53212
                  Attn:  Stock Transfer Administration


         Section 8.3 Governing Law. This Warrant Agreement and the Warrant
Certificates are being delivered in the State of Minnesota and shall be
construed and enforced in accordance with and governed by the laws of such
state.



         Section 8.4 No Benefits Conferred. Nothing in this Warrant Agreement
expressed and nothing that may be implied from any of the provisions hereof is
intended, or shall be construed, to confer upon, or give to, any person or
corporation other than the Company, the Warrant Agent, and the holders of the
Warrant Certificates, any right, remedy or claim under or by reason of this
Warrant Agreement or of any covenant, condition, stipulation, promise or
agreement herein; and all covenants, conditions, stipulations, promises and
agreements in this Warrant Agreement contained shall be for the sole and
exclusive benefit of the Company, the Warrant Agent, their respective successors
and the holders of the Warrant Certificates.


         Section 8.5 Headings. The descriptive headings used in this Warrant
Agreement are inserted for convenience only and shall not control or affect the
meaning or construction of any of the provisions hereof.

         IN WITNESS WHEREOF, this Warrant Agreement has been duly executed by
the parties hereto as of the day and year first above written.

                             HYPERTENSION DIAGNOSTICS, INC.


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



                             FIRSTAR BANK, N.A.


                             By /s/ Keith Maurmeier
                                -------------------------------
                                Its Vice President



                                       14