<PAGE>

                                                                    EXHIBIT 10.4


THIS WARRANT AND THE COMMON SHARES ISSUABLE UPON EXERCISE OF THIS WARRANT HAVE
NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. THIS WARRANT
AND THE COMMON SHARES ISSUABLE UPON EXERCISE OF THIS WARRANT MAY NOT BE SOLD,
OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE
REGISTRATION STATEMENT AS TO THIS WARRANT UNDER SAID ACT OR AN OPINION OF
COUNSEL REASONABLY SATISFACTORY TO HYPERTENSION DIAGNOSTICS, INC. THAT SUCH
REGISTRATION IS NOT REQUIRED.

                                            Right to Purchase 100,000 shares of
                                            Common Stock of Hypertension
                                            Diagnostics, Inc. (subject to
                                            adjustment as provided herein)


                          COMMON STOCK PURCHASE WARRANT

No. 2002-A                                            Issue Date: March 27, 2002

         HYPERTENSION DIAGNOSTICS, INC., a corporation organized under the laws
of Minnesota (the "Company"), hereby certifies that, for value received,
Hyperion Holdings, LLC (the "Holder"), or assigns, is entitled, subject to the
terms set forth below, to purchase from the Company from and after the Issue
Date of this Warrant and at any time or from time to time before 5:00 p.m.,
Minneapolis, Minnesota time, through three (3) years after such date (the
"Expiration Date"), up to 100,000 fully paid and nonassessable shares of Common
Stock (as hereinafter defined), $.01 par value per share, of the Company at a
per share purchase price of ______ per share. The aforedescribed purchase price
per share, as adjusted from time to time as herein provided, is referred to
herein as the "Purchase Price". The number and character of such shares of
Common Stock and the Purchase Price are subject to adjustment as provided
herein.

         As used herein the following terms, unless the context otherwise
requires, have the following respective meanings:

         (a) The term "Company" shall include Hypertension Diagnostics, Inc. and
any corporation which shall succeed or assume the obligations of Hypertension
Diagnostics, Inc. hereunder.

         (b) The term "Common Stock" includes (i) the Company's Common Stock,
$.01 par value per share, (ii) any other capital stock of any class or classes
(however designated) of the Company, authorized on or after such date, the
Holders of which shall have the right, without limitation as to amount, either
to all or to a share of the balance of current dividends and liquidating
dividends after the payment of dividends and distributions on any shares
entitled to preference, and the Holders of which shall ordinarily, in the
absence of contingencies, be entitled to vote for the election of a majority of
directors of the Company (even if the right so to vote has been suspended by the
happening of such a contingency) and (iii) any other securities into which or
for which any of the securities described in (i) or (ii) may be converted or
exchanged pursuant to a plan of recapitalization, reorganization, merger, sale
of assets or otherwise.

         (c) The term "Other Securities" refers to any stock (other than Common
Stock) and other securities of the Company or any other person (corporate or
otherwise) which the Holder of the Warrant at any time shall be entitled to
receive, or shall have received, on the exercise of the Warrant, in lieu of or
in addition to Common Stock, or which at any time shall be issuable or shall
have been issued in exchange for or in replacement of Common Stock or Other
Securities pursuant to Section 3 or otherwise.



                                       1


<PAGE>



         1. Exercise of Warrant.

                  1.1. Number of Shares Issuable upon Exercise. From and after
the date hereof through and including the Expiration Date, the Holder hereof
shall be entitled to receive, upon exercise of this Warrant in whole in
accordance with the terms of subsection 1.2 or upon exercise of this Warrant in
part in accordance with subsection 1.3, shares of Common Stock of the Company,
subject to adjustment pursuant to Section 4.

                  1.2. Full Exercise. This Warrant may be exercised in full by
the Holder hereof by delivery of an original or facsimile copy of the form of
subscription attached as Exhibit A hereto (the "Subscription Form") duly
executed by such Holder and surrender of the original Warrant within seven (7)
days of exercise, to the Company at its principal office, accompanied by
payment, as provided in Section 1.4, in the amount obtained by multiplying the
number of shares of Common Stock for which this Warrant is then exercisable by
the Purchase Price then in effect.

                  1.3. Partial Exercise. This Warrant may be exercised in part
(but not for a fractional share) by surrender of this Warrant in the manner and
at the place provided in subsection 1.2 except that the amount payable by the
Holder on such partial exercise shall be the amount obtained by multiplying (a)
the number of shares of Common Stock designated by the Holder in the
Subscription Form by (b) the Purchase Price then in effect. On any such partial
exercise, the Company, at its expense, will forthwith issue and deliver to or
upon the order of the Holder hereof a new Warrant of like tenor, in the name of
the Holder hereof or as such Holder (upon payment by such Holder of any
applicable transfer taxes) may request, the number of shares of Common Stock for
which such Warrant may still be exercised.

                  1.4. Purchase Price; Payment. Payment may be made either in
(i) cash or by certified or official bank check payable to the order of the
Company equal to the applicable aggregate Purchase Price and the Holder shall
thereupon be entitled to receive the number of duly authorized, validly issued,
fully-paid and non-assessable shares of Common Stock (or Other Securities)
determined as provided herein.

                  1.5. Company Acknowledgment. The Company will, at the time of
the exercise of the Warrant, upon the request of the Holder hereof acknowledge
in writing its continuing obligation to afford to such Holder any rights to
which such Holder shall continue to be entitled after such exercise in
accordance with the provisions of this Warrant. If the Holder shall fail to make
any such request, such failure shall not affect the continuing obligation of the
Company to afford to such Holder any such rights.

                  1.6. Trustee for Warrant Holders. In the event that a bank or
trust company shall have been appointed as trustee for the Holders of the
Warrants pursuant to Subsection 2.2, such bank or trust company shall have all
the powers and duties of a warrant agent (as hereinafter described) and shall
accept, in its own name for the account of the Company or such successor person
as may be entitled thereto, all amounts otherwise payable to the Company or such
successor, as the case may be, on exercise of this Warrant pursuant to this
Section 1.



                                       2


<PAGE>


                  1.7 Delivery of Stock Certificates, etc. on Exercise. The
Company agrees that the shares of Common Stock purchased upon exercise of this
Warrant shall be deemed to be issued to the Holder hereof as the record owner of
such shares as of the close of business on the date on which this Warrant shall
have been surrendered and payment made for such shares as aforesaid. As soon as
practicable after the exercise of this Warrant in full or in part, and in any
event within seven (7) days thereafter, 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 hereof, or as such Holder (upon payment by
such Holder of any applicable transfer taxes) may direct in compliance with
applicable securities laws, a certificate or certificates for the number of duly
and validly issued, fully paid and nonassessable shares of Common Stock (or
Other Securities) to which such Holder shall be entitled on such exercise, plus,
in lieu of any fractional share to which such Holder would otherwise be
entitled, cash equal to such fraction multiplied by the then Fair Market Value
of one full share, together with any other stock or other securities and
property (including cash, where applicable) to which such Holder is entitled
upon such exercise pursuant to Section 1 or otherwise.

         2. Adjustment for Reorganization, Consolidation, Merger, etc.

                  2.1. Reorganization, Consolidation, Merger, etc. In case at
any time or from time to time, the Company shall (a) effect a reorganization,
(b) consolidate with or merge into any other person or (c) transfer all or
substantially all of its properties or assets to any other person under any plan
or arrangement contemplating the dissolution of the Company, then, in each such
case, as a condition to the consummation of such a transaction, proper and
adequate provision shall be made by the Company whereby the Holder of this
Warrant, on the exercise hereof as provided in Section 1, at any time after the
consummation of such reorganization, consolidation or merger or the effective
date of such dissolution, as the case may be, shall receive, in lieu of the
Common Stock (or Other Securities) issuable on such exercise prior to such
consummation or such effective date, the stock and other securities and property
(including cash) to which such Holder would have been entitled upon such
consummation or in connection with such dissolution, as the case may be, if such
Holder had so exercised this Warrant, immediately prior thereto, all subject to
further adjustment thereafter as provided in Section 3.

                  2.2. Dissolution. In the event of any dissolution of the
Company following the transfer of all or substantially all of its properties or
assets, the Company, prior to such dissolution, shall at its expense deliver or
cause to be delivered the stock and other securities and property (including
cash, where applicable) receivable by the Holders of the Warrants after the
effective date of such dissolution pursuant to this Section 2 to a bank or trust
company having its principal office in Minneapolis, Minnesota, as trustee for
the Holder or Holders of the Warrants.

                  2.3. Continuation of Terms. Upon any reorganization,
consolidation, merger or transfer (and any dissolution following any transfer)
referred to in this Section 2, this Warrant shall continue in full force and
effect and the terms hereof shall be applicable to the shares of stock and other
securities and property receivable on the exercise of this Warrant after the
consummation of such reorganization, consolidation or merger or the effective
date of dissolution following any such transfer, as the case may be, and shall
be binding upon the issuer of any such stock or other securities, including, in
the case of any such transfer, the person acquiring all or substantially all of
the properties or assets of the Company, whether or not such person shall have
expressly assumed the terms of this Warrant as provided in Section 4. In the
event this Warrant does not continue in full force and effect after the
consummation of the transaction described in this Section 2, then only in such
event will the Company's securities and property (including cash, where
applicable) receivable by the Holders of the Warrants be delivered to the
Trustee as contemplated by Section 2.2.



                                       3



<PAGE>



         3. Extraordinary Events Regarding Common Stock. In the event that the
Company shall (a) issue additional shares of the Common Stock as a dividend or
other distribution on outstanding Common Stock, (b) subdivide its outstanding
shares of Common Stock or (c) combine its outstanding shares of the Common Stock
into a smaller number of shares of the Common Stock, then, in each such event,
the Purchase Price shall, simultaneously with the happening of such event, be
adjusted by multiplying the then Purchase Price by a fraction, the numerator of
which shall be the number of shares of Common Stock outstanding immediately
prior to such event and the denominator of which shall be the number of shares
of Common Stock outstanding immediately after such event, and the product so
obtained shall thereafter be the Purchase Price then in effect. The Purchase
Price, as so adjusted, shall be readjusted in the same manner upon the happening
of any successive event or events described herein in this Section 3. The number
of shares of Common Stock that the Holder of this Warrant shall thereafter, on
the exercise hereof as provided in Section 1, be entitled to receive shall be
increased to a number determined by multiplying the number of shares of Common
Stock that would otherwise (but for the provisions of this Section 3) be
issuable on such exercise by a fraction of which (a) the numerator is the
Purchase Price that would otherwise (but for the provisions of this Section 3)
be in effect, and (b) the denominator is the Purchase Price in effect on the
date of such exercise.

         4. Certificate as to Adjustments. In each case of any adjustment or
readjustment in the shares of Common Stock (or Other Securities) issuable on the
exercise of the Warrants, the Company at its expense will promptly cause its
Chief Financial Officer or other appropriate designee to compute such adjustment
or readjustment in accordance with the terms of the Warrant and prepare a
certificate setting forth such adjustment or readjustment and showing in detail
the facts upon which such adjustment or readjustment is based, including a
statement of (a) the consideration received or receivable by the Company for any
additional shares of Common Stock (or Other Securities) issued or sold or deemed
to have been issued or sold, (b) the number of shares of Common Stock (or Other
Securities) outstanding or deemed to be outstanding and (c) the Purchase Price
and the number of shares of Common Stock to be received upon exercise of this
Warrant, in effect immediately prior to such adjustment or readjustment and as
adjusted or readjusted as provided in this Warrant. The Company will forthwith
mail a copy of each such certificate to the Holder of the Warrant.

         5. Reservation of Stock, etc. Issuable on Exercise of Warrant;
Financial Statements. From and after forty-five (45) days after the Issue Date
of this Warrant, the Company will at all times reserve and keep available,
solely for issuance and delivery on the exercise of the Warrants, all shares of
Common Stock (or Other Securities) from time to time issuable on the exercise of
the Warrant. This Warrant entitles the Holder hereof to receive copies of all
financial and other information distributed or required to be distributed to the
Holders of the Company's Common Stock.

         6. Assignment; Exchange of Warrant. Subject to compliance with
applicable securities laws, this Warrant, and the rights evidenced hereby, may
be transferred by any registered Holder hereof (a "Transferor") with respect to
any or all of the Shares. On the surrender for exchange of this Warrant, with
the Transferor's endorsement in the form of Exhibit B attached hereto (the
"Transferor Endorsement Form") and together with evidence reasonably
satisfactory to the Company demonstrating compliance with applicable securities
laws, the Company at its expense, but with payment by the Transferor of any
applicable transfer taxes) will issue and deliver to or on the order of the
Transferor thereof a new Warrant or Warrants of like tenor, in the name of the
Transferor and/or the transferee(s) specified in such Transferor Endorsement
Form (each a "Transferee"), calling in the aggregate on the face or faces
thereof for the number of shares of Common Stock called for on the face or faces
of the Warrant so surrendered by the Transferor.



                                       4

<PAGE>



         7. Replacement of Warrant. On receipt of evidence reasonably
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of any such loss, theft or destruction of this
Warrant, on delivery of an indemnity agreement or security reasonably
satisfactory in form and amount to the Company or, in the case of any such
mutilation, on surrender and cancellation of this Warrant, the Company at its
expense will execute and deliver, in lieu thereof, a new Warrant of like tenor.

         8. Registration Rights.

                  8.1 Registration. If, at any time after the date hereof and
prior to the expiration of this Warrant, the Company shall propose to file any
registration statement under the Securities Act of 1933, as amended, (the "ACT")
covering a public offering of the Company's Common Stock (other than a
registration on Form S-4, Form S-8 or any registration form that does not permit
secondary sales or a registration of the Warrant Shares), it will notify the
holder hereof in writing at least twenty (20) days prior to each such filing and
will include in the registration statement (to the extent permitted by
applicable regulation) the Common Stock purchased by the holder or purchasable
by the holder upon the exercise of the Warrant to the extent requested by the
holder hereof. Notwithstanding the foregoing, the number of shares of the
holders of the Warrants proposed to be registered thereby shall be reduced pro
rata with any other selling shareholder (other than the Company) upon the
request of the managing underwriter of such offering. If the registration
statement or offering statement filed pursuant to such twenty (20) day notice
has not become effective within six months following the date such notice is
given to the holder hereof, the Company must again notify such holder in the
manner provided above.

                  8.2 Expenses. All expenses of any such registrations referred
to in this Section 8, except the fees of counsel or other professional advisors
to such holders and underwriting commissions or discounts shall be borne by the
Company.

                  8.3 Notice.The Company will mail to each record holder, at the
last known post office address, written notice of any exercise of the rights
granted under this Section 8, by certified or registered mail, return receipt
requested, and each holder shall have ten (10) days from the date of deposit of
such notice in the U.S. Mail to notify the Company in writing whether such
holder wishes to join in such exercise.

                  8.4 Prospectus;Effectiveness. The Company will furnish the
holder hereof with a reasonable number of copies of any prospectus included in
such filings and will amend or supplement the same as required during the period
of required use thereof. The Company will maintain the effectiveness of any
registration statement or the offering statement filed by the Company, whether
or not at the request of the holder hereof, for at least six (6) months
following the effective date thereof.

                  8.5 Indemnification. In the case of the filing of any
registration statement, and to the extent permissible under the Act and
controlling precedent thereunder, the Company and the holder hereof shall
provide cross indemnification agreements to each other in customary scope
covering the accuracy and completeness of the information furnished by each.

                  8.6 Co-operation. The Holder of the Warrant agrees to
cooperate with the Company in the preparation and filing of any such
registration statement or offering statement, and in the furnishing of
information concerning the holder for inclusion therein, or in any efforts by
the Company to establish that the proposed sale is exempt under the Act as to
any proposed distribution.


         9. Maximum Exercise. The Holder shall not be entitled to exercise this
Warrant on an exercise date, in connection with that number of shares of Common
Stock which would be in excess of the sum of (i) the number of shares of Common
Stock beneficially owned by the Holder and its affiliates on an exercise date,



                                       5



<PAGE>



and (ii) the number of shares of Common Stock issuable upon the exercise of this
Warrant with respect to which the determination of this limitation is being made
on an exercise date, which would result in beneficial ownership by the Holder
and its affiliates of more than 4.99% of the outstanding shares of Common Stock
of the Company on such date. For the purposes of the immediately preceding
sentence, beneficial ownership shall be determined in accordance with Section
13(d) of the Securities Exchange Act of 1934, as amended, and Regulation 13d-3
thereunder. Subject to the foregoing, the Holder shall not be limited to
aggregate exercises which would result in the issuance of more than 4.99%. The
restriction described in this paragraph may be revoked upon seventy-five (75)
days prior notice from the Holder to the Company. The Holder may allocate which
of the equity of the Company deemed beneficially owned by the Subscriber shall
be included in the 4.99% amount described above and which shall be allocated to
the excess above 4.99%.

         10. Transfer on the Company's Books. Until this Warrant is transferred
on the books of the Company, the Company may treat the registered Holder hereof
as the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary.

         11. Notices. All notices and other communications from the Company to
the Holder of this Warrant shall be mailed by first class registered or
certified mail, postage prepaid, at such address as may have been furnished to
the Company in writing by such Holder or, until any such Holder furnishes to the
Company an address, then to, and at the address of, the last Holder of this
Warrant who has so furnished an address to the Company.

         12. Miscellaneous. This Warrant and any term hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought. This Warrant shall be construed and enforced in accordance with and
governed by the laws of Minnesota. Any dispute relating to this Warrant shall be
adjudicated in Hennepin County in the State of Minnesota. The headings in this
Warrant are for purposes of reference only, and shall not limit or otherwise
affect any of the terms hereof. The invalidity or unenforceability of any
provision hereof shall in no way affect the validity or enforceability of any
other provision.


                             [signatures next page]





                                       6


<PAGE>


                   IN WITNESS WHEREOF, the Company has executed this Warrant as
of the date first written above.


                                         HYPERTENSION DIAGNOSTICS, INC.
                                         a Minnesota corporation



                                         By:
                                             -----------------------------------
                                             Greg H. Guettler, President

Witness:



---------------------------------





                                       7

<PAGE>


                                    EXHIBIT A

                              FORM OF SUBSCRIPTION
                   (to be signed only on exercise of Warrant)

TO:  HYPERTENSION DIAGNOSTICS, INC.

The undersigned, pursuant to the provisions set forth in the attached Warrant
(No.____), hereby irrevocably elects to purchase:

___________ shares of the Common Stock covered by such Warrant

The undersigned herewith makes payment of the full purchase price for such
shares at the price per share provided for in such Warrant, which is
$___________, in lawful money of the United States

The undersigned requests that the certificates for such shares be issued in the
name of, and delivered to _____________________________________________________
whose address is ______________________________________________________________
_______________________________________________________________________________

The undersigned represents and warrants that all offers and sales by the
undersigned of the securities issuable upon exercise of the within Warrant shall
be made pursuant to registration of the Common Stock under the Securities Act of
1933, as amended (the "Securities Act"), or pursuant to an exemption from
registration under the Securities Act.

Dated:___________________                ______________________________________
                                         (Signature must conform to name of
                                         Holder as specified on the face of the
                                         Warrant)


                                         _______________________________________

                                         _______________________________________
                                         (Address)




                                       8

<PAGE>


                                    EXHIBIT B


                         FORM OF TRANSFEROR ENDORSEMENT
                   (To be signed only on transfer of Warrant)

                  For value received, the undersigned hereby sells, assigns, and
transfers unto the person(s) named below under the heading "Transferees" the
right represented by the within Warrant to purchase the percentage and number of
shares of Common Stock of HYPERTENSION DIAGNOSTICS, INC. to which the within
Warrant relates specified under the headings "Percentage Transferred" and
"Number Transferred," respectively, opposite the name(s) of such person(s) and
appoints each such person Attorney to transfer its respective right on the books
of HYPERTENSION DIAGNOSTICS, INC. with full power of substitution in the
premises.

<TABLE>
<CAPTION>
---------------------------------------- -------------------------------------- --------------------------------------
              Transferees                       Percentage Transferred                   Number Transferred
---------------------------------------- -------------------------------------- --------------------------------------
<S>                                      <C>                                    <C>
---------------------------------------- -------------------------------------- --------------------------------------

---------------------------------------- -------------------------------------- --------------------------------------

---------------------------------------- -------------------------------------- --------------------------------------
</TABLE>


Dated:  ______________, _________        _______________________________________
                                         (Signature must conform to name of
                                         Holder as specified on the face of the
                                         warrant)

Signed in the presence of:

_________________________________        _______________________________________
            (Name)
                                         _______________________________________
                                                       (address)

ACCEPTED AND AGREED:
[TRANSFEREE]                             _______________________________________

                                         _______________________________________
                                                       (address)
_________________________________
            (Name)





                                       9