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                                                                     EXHIBIT 4.1


                            UGLY DUCKLING CORPORATION

                                WARRANT AGREEMENT

         THIS WARRANT AGREEMENT (the "Agreement"), dated as of February 9, 1998,
is by and among UGLY DUCKLING CORPORATION, a Delaware corporation (the
"Company"), RELIANCE ACCEPTANCE GROUP, INC., a Delaware corporation
("Reliance"), and HARRIS TRUST COMPANY OF CALIFORNIA, as warrant agent (the
"Warrant Agent").

         WHEREAS, the Company has entered into an Agreement dated as of February
9, 1998 (the "Servicing Agreement"), by and among the Company, Reliance,
Reliance Acceptance Corporation, a Delaware corporation, and BankAmerica
Business Credit, Inc., a Delaware corporation, as agent on behalf of itself and
other lenders, pursuant to which the Company has agreed to service certain motor
vehicle retail installment sale contracts of Reliance, all as set forth in, and
subject to the terms and conditions of, the Servicing Agreement; and

         WHEREAS, pursuant to the Servicing Agreement, the Company has agreed to
issue to Reliance warrants (the "Warrants") to purchase shares of common stock,
$.001 par value per share ("Common Stock"), of the Company, subject to the terms
and conditions of this Agreement; and

         WHEREAS, the Company desires the Warrant Agent to act on behalf of the
Company, and the Warrant Agent is willing so to act, in connection with the
issuance, registration, transfer, exchange, exercise, and redemption of the
Warrants.

         NOW, THEREFORE, in consideration of the promises and the mutual
agreements herein set forth, the parties agree as follows:

         Section 1. APPOINTMENT OF WARRANT AGENT. The Company hereby appoints
the Warrant Agent to act as agent of the Company in accordance with the terms
and conditions set forth in this Agreement, and the Warrant Agent hereby accepts
such appointment.

         Section 2. ISSUANCE OF WARRANTS AND FORM OF WARRANTS.

         (a) Subject to the terms and conditions hereof, the Company shall issue
to Reliance, as reorganized upon consummation of Reliance's Joint Plan of
Reorganization dated February 9, 1998, as amended (the "Plan"), or any
transferee of Reliance approved by the Company (an "approved transferee"), and
Reliance or any such approved transferee shall accept from the Company, Warrants
substantially in the form attached hereto as Exhibit A. For purposes of this
Agreement, the term "Reliance" shall include any approved transferee or
Reliance, as reorganized upon consummation of (the Plan). Reliance will be
entitled to receive Warrants to purchase shares of Common Stock of the Company
in the amounts and at the times set forth on Exhibit B hereto.
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         (b) Each Warrant shall entitle the registered holder of the certificate
representing such Warrant to purchase upon the exercise thereof one share of
Common Stock, subject to the adjustments provided for in Section 9 hereof, at
any time until 5:00 p.m., New York City time, on the date that is three years
after the date of its initial issuance.

         (c) The Warrant certificates shall be in registered form only. Each
Warrant certificate shall be dated by the Warrant Agent as of the date of
issuance thereof (whether upon initial issuance or upon transfer or exchange),
and shall be executed on behalf of the Company by the manual or facsimile
signature of its President or a Vice President, and attested to by the manual or
facsimile signature of its Secretary or an Assistant Secretary. In case any
officer of the Company who shall have signed any Warrant certificate shall cease
to be such officer of the Company before such Warrant Certificate has been
countersigned by the Warrant Agent or prior to the issuance thereof, such
Warrant certificate may nevertheless be issued and delivered with the same force
and effect as though the person who signed the same had not ceased to be such
officer of the Company.

         Section 3. EXERCISE OF WARRANTS, DURATION AND WARRANT PRICE. Subject to
the provisions of this Agreement, each registered holder of one or more Warrant
certificates shall have the right, which may be exercised as provided in such
Warrant certificates, to purchase from the Company (and the Company shall issue
and sell to such registered holder) the number of shares of Common Stock or
other securities to which the Warrants represented by such certificates are at
the time entitled hereunder.

         (a) Each Warrant not exercised by its expiration date shall become
void, and all rights thereunder and all rights in respect thereof under this
Agreement shall cease on such date.

         (b) A Warrant may be exercised by the surrender of the certificate
representing such Warrant to the Company, at the office of the Warrant Agent, or
at the office of a successor to the Warrant Agent, with the subscription form
set forth on the reverse thereof duly executed and properly endorsed with the
signatures properly guaranteed, and upon payment in full to the Warrant Agent
for the account of the Company of the Warrant Price (as hereinafter defined) for
the number of shares of Common Stock or other securities as to which the Warrant
is exercised. Such Warrant Price shall be paid in full either (i) in cash, or by
certified check or bank draft payable in United States currency to the order of
the Warrant Agent or (ii) delivery of a written notice to the Company and the
Warrant Agent that the holder is exercising the Warrant (or a portion thereof)
by authorizing the Warrant Agent on behalf of the Company to withhold from
issuance a number of shares of Common Stock issuable upon such exercise of the
Warrant, which, when multiplied by the Current Market Price (as such term is
defined in Section 10 hereof) of the Common Stock as of the date of exercise, is
equal to the Warrant Price (as defined in Section 3(c) hereof) for the number of
shares of Common Stock or other securities as to which the Warrant is exercised
(and such withheld shares shall no longer be issuable under this Warrant
Agreement).


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         (c) Subject to adjustment in accordance with Section 9 hereof, the
price per share of Common Stock at which each Warrant may be exercised (the
"Warrant Price") shall be $12.50 for the first 150,000 Warrants issued and the
greater of $12.50 or 120% of the Market Price of the Common Stock as of the date
of issuance of the Warrants for all Warrants issued thereafter. For purposes of
this Section 3(c), the term "Market Price" shall mean (i) if the Common Stock is
quoted on the Nasdaq National Market or the Nasdaq SmallCap Market or on a
national securities exchange, the average of the daily per share closing prices
of the Common Stock as quoted on the Nasdaq National Market or the Nasdaq
SmallCap Market or on the principal stock exchange on which it is listed for the
10 consecutive trading days ending on the third trading day prior to the date of
issuance of the Warrants in question, or (ii) if the Common Stock is traded in
the over-the-counter market and not quoted on the Nasdaq National Market or the
Nasdaq SmallCap Market nor on any national securities exchange, the average of
the daily closing bid prices of the Common Stock for the 10 consecutive trading
days ending on the third trading day prior to the date of issuance of the
Warrants in question, as reported by Nasdaq or an equivalent generally accepted
reporting service. The closing price referred to in clause (i) above shall be
the last reported sale price or, in case no such reported sale takes place on
such day, the average of the reported closing bid and asked prices, in either
case on the Nasdaq National Market or the Nasdaq SmallCap Market or on the
national securities exchange on which the Common Stock is then listed. For
purposes of clause (ii) above, if trading in the Common Stock is not reported by
Nasdaq, the bid price referred to in said clause shall be the lowest bid price
as quoted on the OTC Bulletin Board or reported in the "pink sheets" published
by National Quotation Bureau, Incorporated. If the Market Price cannot be
calculated in accordance with any of the procedures described above, the Market
Price shall be the fair market value of the Common Stock on the applicable date
of determination as reasonably determined by an investment banking firm selected
by the holder and reasonably acceptable to the Company, with the costs of such
appraisal to be borne by the Company.

         (d) Subject to the further provisions of this Section 3 and of Section
6 hereof, upon surrender of Warrant certificates and payment of the Warrant
Price or other consideration for exercise pursuant to Section 3(b) hereof, the
Company shall issue and cause to be delivered, as promptly as practicable to or
upon the written order of the registered holder of such Warrants and in such
name or names as such registered holder may designate, subject to applicable
securities laws, a certificate or certificates for the number of securities so
purchased upon the exercise of such Warrants, together with cash, as provided in
Section 10 of this Agreement, in respect of any fraction of a share or security
otherwise issuable upon such surrender. All shares of Common Stock or other such
securities issued upon the exercise of a Warrant shall be duly authorized,
validly issued, fully paid and nonassessable and free and clear of all liens and
other encumbrances.

         (e) Certificates representing such securities shall be deemed to have
been issued and any person so designated to be named therein shall be deemed to
have become a holder of record of such securities as of the date of the
surrender of such Warrants and payment of the Warrant Price or other
consideration for exercise pursuant to Section 3(b) hereof; provided, however,
that


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if, at the date of surrender of such Warrants and payment of such Warrant Price
or other consideration, the transfer books for the Common Stock or other
securities purchasable upon the exercise of such Warrants shall be closed, the
certificates for the securities in respect of which such Warrants are then
exercised shall be issuable as of the date on which such books shall next be
opened and until such date the Company shall be under no duty to deliver any
certificate for such securities and the person to whom such securities are
issuable shall not be deemed to have become a holder of record of such
securities. The rights of purchase represented by each Warrant certificate shall
be exercisable, at the election of the registered holder thereof, either as an
entirety or from time to time for part of the number of securities specified
therein and, in the event that any Warrant certificate is exercised in respect
of less than all of the securities specified therein at any time prior to the
expiration date of the Warrant certificate, a new Warrant certificate or
certificates will be issued to such registered holder for the remaining number
of securities specified in the Warrant certificate so surrendered.

         Section 4. COUNTERSIGNATURE AND REGISTRATION.

         (a) The Warrant Agent shall maintain books (the "Warrant Register") for
the registration and the registration of transfer of the Warrants. Upon the
initial issuance of the Warrants, the Warrant Agent shall issue and register the
Warrants in the name of Reliance in accordance with Section 2 hereof. The
Warrant certificates shall be countersigned manually or by facsimile by the
Warrant Agent (or by any successor to the Warrant Agent then acting as such
under this Agreement) and shall not be valid for any purpose unless so
countersigned. Warrant certificates may be so countersigned, however, by the
Warrant Agent and delivered by the Warrant Agent, notwithstanding that the
persons whose manual or facsimile signatures appear thereon as proper officers
of the Company shall have ceased to be such officers at the time of such
countersignature or delivery.

         (b) Prior to due presentment for registration of transfer of any
Warrant certificate, the Company and the Warrant Agent may deem and treat the
person in whose name such Warrant certificate shall be registered upon the
Warrant Register (the "registered holder") as the absolute owner of such Warrant
certificate and of each Warrant represented thereby (notwithstanding any
notation of ownership or other writing on the Warrant certificate made by anyone
other than the Company or the Warrant Agent), for the purpose of any exercise
thereof, of any distribution or notice to the holder thereof, and for all other
purposes, and neither the Company nor the Warrant Agent shall be affected by any
notice to the contrary.

         Section 5. TRANSFER AND EXCHANGE OF WARRANTS.

         (a) The Warrant Agent shall register the transfer, from time to time,
of any outstanding Warrant or portion thereof upon the Warrant Register, upon
surrender of the certificate evidencing such Warrant for transfer, properly
endorsed with signatures properly guaranteed and accompanied by appropriate
instructions for transfer. Upon any such transfer, a new Warrant certificate
representing an equal aggregate number of Warrants so transferred shall


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be issued to the transferee and the surrendered Warrant certificate shall be
canceled by the Warrant Agent. In the event that only a portion of a Warrant is
transferred at any time, a new Warrant certificate representing the remaining
portion of the Warrant will also be issued to the transferring holder. The
Warrant certificates so canceled shall be delivered by the Warrant Agent to the
Company from time to time upon written request. Notwithstanding anything to the
contrary herein, no transfer or exchange may be made except in compliance with
applicable securities laws and Section 13 hereof.

         (b) Warrant certificates may be surrendered to the Warrant Agent,
together with a written request for exchange, and thereupon the Warrant Agent
shall issue in exchange therefor one or more new Warrant certificates as
requested by the registered holder of the Warrant certificate or certificates so
surrendered, representing an equal aggregate number of Warrants.

         (c) The Warrant Agent shall not be required to effect any registration
of transfer or exchange which will result in the issuance of a Warrant
certificate for a fraction of a Warrant.

         (d) No service charge shall be made for any exchange or registration of
transfer of Warrant certificates.

         (e) The Warrant Agent is hereby authorized to countersign and to
deliver, in accordance with the terms of this Agreement, the new Warrant
certificates required to be issued pursuant to the provisions hereof, and the
Company, whenever required by the Warrant Agent, will supply the Warrant Agent
with certificates duly executed on behalf of the Company for such purpose.

         Section 6. PAYMENT OF TAXES. The Company will pay any documentary stamp
taxes attributable to the initial issuance or delivery of the shares of Common
Stock or other securities issuable upon the exercise of Warrants; provided,
however, the Company shall not be required to pay any tax or taxes which may be
payable in respect of any transfer of the Warrants or involved in the issuance
or delivery of any Warrant certificate or certificates for shares of Common
Stock in a name other than the registered holder of Warrants in respect of which
such shares are issued, and in such case neither the Company nor the Warrant
Agent shall be required to issue or deliver any certificate for shares of Common
Stock or any Warrant certificate until the person requesting the same has paid
to the Company the amount of such tax or has established to the Company's
satisfaction that such tax has been paid.

         Section 7. MUTILATED OR MISSING WARRANTS. In case any of the Warrant
certificates shall be mutilated, lost, stolen or destroyed, the Company may
issue, and the Warrant Agent shall countersign and deliver in exchange and
substitution for and upon cancellation of the mutilated Warrant certificate, or
in lieu of and substitution for the Warrant certificate lost, stolen or
destroyed, a new Warrant certificate representing an equal aggregate number of
Warrants, but only upon receipt of evidence satisfactory to the Company and the
Warrant Agent of such loss, theft or destruction of such Warrant certificate and
reasonable indemnity, if requested, also


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satisfactory to them. Applicants for such substitute Warrant certificates shall
also comply with such other reasonable conditions and pay such reasonable
charges as the Company or the Warrant Agent may prescribe.

         Section 8. RESERVATION OF COMMON STOCK.

         (a) There have been reserved, and the Company shall at all times keep
reserved, out of its authorized and unissued shares of Common Stock, a number of
shares sufficient to provide for the exercise of the rights of purchase
represented by the Warrants then outstanding or issuable upon exercise, and the
transfer agent for the Common Stock and every subsequent transfer agent for any
shares of the Company's capital stock issuable upon the exercise of any of the
rights of purchase aforesaid are hereby irrevocably authorized and directed at
all times to reserve such number of authorized and unissued shares as shall be
requisite for such purpose. The Company will keep a copy of this Agreement on
file with the transfer agent for the Common Stock and with every subsequent
transfer agent for any shares of the Company's capital stock issuable upon the
exercise of the rights of purchase represented by the Warrants.

         (b) The Warrant Agent is hereby irrevocably authorized to requisition
from time to time from such transfer agent stock certificates required to honor
outstanding Warrants. The Company will supply such transfer agent with duly
executed certificates for such purpose and will itself provide or otherwise make
available any cash as provided in Section 10 of this Agreement. All Warrant
certificates surrendered in the exercise of the rights thereby evidenced shall
be canceled by the Warrant Agent and shall thereafter be delivered to the
Company. Promptly after the expiration date of the Warrants, the Warrant Agent
shall certify to the Company the aggregate number of such Warrants which expired
unexercised, and after the expiration date of the Warrants, no shares of Common
Stock shall be subject to reservation in respect of such Warrants.

         Section 9. ADJUSTMENT OF WARRANT PRICE AND NUMBER OF SHARES OF COMMON
STOCK. The number and kind of securities purchasable upon the exercise of the
Warrants and the Warrant Price shall be subject to adjustment from time to time
upon the happening of certain events, as follows:

         9.1 ADJUSTMENTS. The number of shares of Common Stock or other
securities purchasable upon the exercise of each Warrant and the Warrant Price
shall be subject to adjustment as follows:

                  (a) If the Company (i) pays a dividend in Common Stock or
makes a distribution in Common Stock, (ii) subdivides its outstanding Common
Stock into a greater number of shares, (iii) combines its outstanding Common
Stock into a smaller number of shares, or (iv) issues, by reclassification of
its Common Stock, other securities of the Company, then the number and kind of
shares of Common Stock or other securities purchasable upon exercise of a
Warrant immediately prior thereto will be adjusted so that the holder of a
Warrant will be entitled


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to receive the kind and number of shares of Common Stock or other securities of
the Company that such holder would have owned and would have been entitled to
receive immediately after the happening of any of the events described above,
had the Warrant been exercised immediately prior to the happening of such event
or any record date with respect thereto. Any adjustment made pursuant to this
subsection 9.1(a) will become effective immediately after the effective date of
such event retroactive to the record date, if any, for such event.

                  (b) If at any time there shall be a capital reorganization of
the Company's Common Stock (other than a combination, reclassification,
exchange, or subdivision of shares provided for elsewhere above) or merger or
consolidation of the Company with or into another corporation, or the sale of
the Company's properties and assets as, or substantially as, an entirety to any
other person, then, as a part of such reorganization, merger, consolidation or
sale, lawful provision shall be made so that the holder of this Warrant shall
thereafter be entitled to receive upon exercise of this Warrant, during the
period specified in this Warrant and upon payment of the Warrant Price then in
effect, the number of shares of Common Stock or other securities or property of
the Company, or of the successor corporation resulting from such merger or
consolidation, to which a holder of the Common Stock deliverable upon exercise
of this Warrant would have been entitled in such capital reorganization, merger,
or consolidation or sale if this Warrant had been exercised immediately before
that capital reorganization, merger, consolidation, or sale. In any such case,
appropriate adjustment (as determined in good faith by the Company's Board of
Directors) shall be made in the application of the provisions of this Warrant
with respect to the rights and interests of the holder of this Warrant after the
reorganization, merger, consolidation, or sale to the end that the provisions of
this Warrant (including adjustment of the Warrant Price then in effect and
number of shares purchasable upon exercise of this Warrant) shall be applicable
after that event, as near as reasonably may be, in relation to any shares or
other property deliverable after that event upon exercise of this Warrant.

                  (c) No adjustment in the number of shares or securities
purchasable pursuant to the Warrants shall be required unless such adjustment
would require an increase or decrease of at least one percent in the number of
shares or securities then purchasable upon the exercise of the Warrants;
provided that, upon the occurrence of an adjustment hereunder any time after an
event occurs which would, but for this subsection 9.1(c) require an adjustment
hereunder, such adjustment will be increased or decreased to give effect to the
adjustment that would have been made absent this subsection 9.1(c).

                  (d) Whenever the number of shares or securities purchasable
upon the exercise of the Warrants is adjusted, as herein provided, the Warrant
Price for shares payable upon exercise of the Warrants shall be adjusted by
multiplying such Warrant Price immediately prior to such adjustment by a
fraction, the numerator of which shall be the number of shares purchasable upon
the exercise of the Warrant immediately prior to such adjustment, and the
denominator of which shall be the number of shares so purchasable immediately
thereafter.


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                  (e) Whenever the number of shares or securities purchasable
upon the exercise of the Warrants and/or the Warrant Price is adjusted as herein
provided, the Company shall cause to be promptly mailed to the Warrant Agent and
each registered holder of a Warrant by first class mail, postage prepaid, notice
of such adjustment and a certificate of the chief financial officer of the
Company setting forth the number of shares or securities purchasable upon the
exercise of the Warrants after such adjustment, the Warrant Price as adjusted, a
brief statement of the facts requiring such adjustment and the computation by
which such adjustment was made. The Warrant Agent shall be fully protected in
relying on any such certificate and any adjustment therein contained, and shall
not be obligated or responsible for calculating any adjustment nor shall it be
deemed to have knowledge of such an adjustment unless and until it shall have
received such certificate.

                  (f) For the purpose of this subsection 9.1, the term "Common
Stock" shall mean (i) the class of stock designated as the voting Common Stock
of the Company at the date of this Agreement, or (ii) any other class of stock
or securities resulting from successive changes or reclassifications of such
Common Stock consisting solely of changes in par value, or from par value to no
par value, or from no par value to par value. In the event that at any time, as
a result of an adjustment made pursuant to this Section 9, a registered holder
shall become entitled to purchase any securities of the Company other than
shares of Common Stock, thereafter the number of such other securities so
purchasable upon exercise of the Warrants shall be subject to adjustment from
time to time in a manner and on terms as nearly equivalent as practicable to the
provisions with respect to the shares contained in this Section 9.

         9.2 NO ADJUSTMENT FOR DIVIDENDS. Except as provided in Subsection 9.1,
no adjustment in respect of any dividends or distributions shall be made during
the term of the Warrants or upon the exercise of the Warrants.

         9.3 NO ADJUSTMENT IN CERTAIN CASES. No adjustments are required to be
made pursuant to Section 9 hereof upon the issuance of shares of Common Stock or
the Warrants (or the underlying shares of Common Stock) required hereunder or
pursuant to the Agreement of Understanding dated as of February 9, 1998 between
the Company and Reliance or the Servicing Agreement.

         9.4 PRESERVATION OF PURCHASE RIGHTS UPON RECLASSIFICATION,
CONSOLIDATION, ETC. In case of any consolidation of the Company with or merger
of the Company into another corporation or in case of any sale or conveyance to
another corporation of the property, assets or business of the Company as an
entirety or substantially as an entirety, the Company or such successor or
purchasing corporation, as the case may be, shall execute with the Warrant Agent
an agreement that the registered holders of the Warrants shall have the right
thereafter, upon payment of the Warrant Price in effect immediately prior to
such action, to purchase, upon exercise of each Warrant, the kind and amount of
shares and other securities and property which it would have owned or have been
entitled to receive after the happening of such consolidation, merger, sale or
conveyance had each Warrant been exercised immediately prior to such action.


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Any such agreements referred to in this subsection 9.4 shall provide for
adjustments, which shall be as nearly equivalent as may be practicable to the
adjustments provided for in Section 9 hereof. The provisions of this subsection
9.4 shall similarly apply to successive consolidations, mergers, sales, or
conveyances.

         9.5 PAR VALUE OF SHARES OF COMMON STOCK. Before taking any action that
would cause an adjustment reducing the Warrant Price below the then par value of
the Common Stock issuable upon exercise of the Warrants, the Company will take
any corporate action which may, in the opinion of its counsel, be necessary in
order that the Company may validly and legally issue fully paid and
nonassessable Common Stock at such adjusted Warrant Price.

         9.6 INDEPENDENT PUBLIC ACCOUNTANTS. The Company may but shall not be
required to retain a firm of independent public accountants of recognized
regional or national standing (which may be any such firm regularly employed by
the Company) to make any computation required under this Section 9, and a
certificate signed by such firm shall be conclusive evidence of the correctness
of any computation made under this Section 9 and the Company shall cause to be
promptly mailed to the Warrant Agent and each registered holder of a Warrant by
first class mail, postage prepaid, a copy of such certificate.

         9.7 STATEMENT ON WARRANT CERTIFICATES. Irrespective of any adjustments
in the Warrant Price or the number of securities issuable upon exercise of
Warrants, Warrant certificates theretofore or thereafter issued may continue to
express the same price and number of securities as are stated in the similar
Warrant certificates initially issuable pursuant to this Agreement. However, the
Company may, at any time in its sole discretion (which shall be conclusive),
make any change in the form of Warrant certificate that it may deem appropriate
and that does not affect the substance thereof; and any Warrant certificate
thereafter issued, whether upon registration of, transfer of, or in exchange or
substitution for, an outstanding Warrant certificate, may be in the form so
changed.

         9.8 NO RIGHTS AS STOCKHOLDER; NOTICES TO HOLDERS OF WARRANTS. If, at
any time prior to the expiration of a Warrant and prior to its exercise, any one
or more of the following events shall occur:

                  (a) any action that would require an adjustment pursuant to
subsection 9.1 or 9.4 hereof; or

                  (b) a dissolution, liquidation or winding up of the Company
(other than in connection with a consolidation, merger or sale of its property,
assets and business as an entirety or substantially as an entirety) shall be
proposed; then the Company must give notice in writing of such event to the
registered holders of the Warrants, as provided in Section 20 hereof, at least
20 days, to the extent practicable, prior to the date fixed as a record date or
the date of closing the transfer books for the determination of the stockholders
entitled to any relevant dividend, distribution, subscription rights or other
rights or for the determination of stockholders entitled to


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vote on such proposed dissolution, liquidation or winding up. Such notice must
specify such record date or the date of closing the transfer books, as the case
may be. Failure to mail or receive such notice or any defect therein will not
affect the validity of any action taken with respect thereto.

         Section 10. FRACTIONAL INTERESTS. The Company is not required to issue
fractional shares of Common Stock on the exercise of a Warrant. If any fraction
of a share of Common Stock would, except for the provisions of this Section 10,
be issuable on the exercise of a Warrant (or specified portion thereof), the
Company will in lieu thereof pay an amount in cash equal to the then Current
Market Price for the business day immediately preceding the date of issuance
multiplied by such fraction. For purposes of this Agreement, the term "Current
Market Price" means (i) if the Common Stock is listed for quotation on the
Nasdaq National Market or the Nasdaq SmallCap Market or on a national securities
exchange, the per share closing price of the Common Stock on the date of
determination as quoted by the Nasdaq National Market or the Nasdaq SmallCap
Market or on the principal stock exchange on which it is listed, as the case may
be, whichever is the higher, or (ii) if the Common Stock is traded in the
over-the-counter market and is not listed for quotation on the Nasdaq National
Market or the Nasdaq SmallCap Market nor on any national securities exchange,
the per share closing bid price of the Common Stock on the date of
determination, as reported by Nasdaq or an equivalent generally accepted
reporting service. The closing price referred to in clause (i) above shall be
the last reported sale price or, in case no such reported sale takes place on
such day, the average of the reported closing bid and asked prices, in either
case as quoted by the Nasdaq National Market or the Nasdaq SmallCap Market or on
the national securities exchange on which the Common Stock is then listed. For
purposes of clause (ii) above, if trading in the Common Stock is not reported by
Nasdaq, the bid price referred to in said clause shall be the lowest bid price
as reported on the OTC Bulletin Board or in the "pink sheets" published by
National Quotation Bureau, Incorporated. If the Current Market Price cannot be
calculated in accordance with any of the procedures described above, the Current
Market Price shall be the fair market value of the Common Stock on the
applicable date of determination as reasonably determined by an investment
banking firm selected by the holder and reasonably acceptable to the Company,
with the costs of such appraisal to be born by Company.

         Section 11. RIGHTS AS WARRANTHOLDERS. Nothing contained in this
Agreement or in any of the Warrants shall be construed as conferring upon the
holders thereof, as such, any of the rights of stockholders of the Company,
including, without limitation, the right to receive dividends or other
distributions, to exercise any preemptive rights, to vote or to consent or to
receive notice as stockholders in respect of the meetings of stockholders or the
election of directors of the Company or any other matter.

         Section 12. DISPOSITION OF PROCEEDS ON EXERCISE OF WARRANTS. The
Warrant Agent must account promptly to the Company with respect to Warrants
exercised, and must promptly pay to the Company all monies received by it upon
the exercise of such Warrants, and agrees to


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keep copies of this Agreement available for inspection by holders of Warrants
during normal business hours.

         Section 13. RESTRICTIONS ON TRANSFER; REGISTRATION RIGHTS.

         (a) Each holder of a Warrant agrees that prior to making any
disposition or transfer of the Warrants or shares issuable upon exercise of the
Warrants ("Shares"), unless a registration statement under the Securities Act of
1933, as amended (the "Securities Act"), is in effect with regard thereto and
the disposition may be effected in accordance therewith and with applicable
state securities laws, the holder shall give written notice to the Company
describing briefly the manner in which any such proposed disposition or transfer
is to be made; and no such disposition shall be made except pursuant to an
exemption from the registration requirements of all applicable federal and state
securities laws, with the Company entitled to receive an opinion of counsel
(which counsel shall be Kirkland & Ellis or such other counsel reasonably
satisfactory to the Company) prior to the effectuation of any such disposition
or transfer.

         (b) Each certificate evidencing the Warrants shall bear a legend in
substantially the following form, and each certificate evidencing Shares
issuable upon exercise of the Warrants shall bear such a legend until such time
as such Shares have been sold pursuant to a registration statement contemplated
in subsection (c) below or unless, in the opinion of legal counsel to the
Company, such legend is not required in order to establish compliance with any
provisions of applicable security laws:

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
         UNDER THE SECURITIES ACT OF 1933 OR ANY STATE SECURITIES LAWS AND MAY
         NOT BE SOLD, EXCHANGED, HYPOTHECATED OR OTHERWISE TRANSFERRED IN ANY
         MANNER EXCEPT IN COMPLIANCE WITH SECTION 13 OF THE WARRANT AGREEMENT
         DATED AS OF FEBRUARY 9, 1998, BETWEEN UGLY DUCKLING CORPORATION AND
         HARRIS TRUST COMPANY OF CALIFORNIA, AS WARRANT AGENT, AS THE SAME MAY
         BE AMENDED FROM TIME TO TIME.

         (c) Subject to the next sentence below, whenever during the one-year
period beginning on each date that the Warrants issued hereunder become
exercisable the Company proposes to file with the Commission a registration
statement with respect to equity securities of the Company (other than as to
securities issued pursuant to an employee benefit plan or as to a transaction
subject to Rule 145 promulgated under the Securities Act or for which a Form S-4
Registration Statement could be used), it shall, at least 30 days prior to such
filing, give written notice of such proposed filing to the holders of Warrants
then exercisable and Shares which bear a legend as contemplated in Section 13(b)
above and which shall not have previously been included in a registration
statement filed under this Section 13(c), at their respective addresses as


                                       11
<PAGE>   12
they appear on the records of the Warrant Agent or the Company, and shall offer
to include and shall include, subject to the provisions of this Section 13(c),
in such filing any proposed disposition of such Shares upon receipt by the
Company, not less than 10 days prior to the proposed filing date, of a request
therefor setting forth the facts with respect to such proposed disposition and
all other information with respect to the holders of such Warrants or the Shares
requested to be included in such filing as shall be reasonably necessary to be
included in such Registration Statement. Notwithstanding the above, after such
time as the holders shall have been given two opportunities to include their
Shares in a Registration Statement of the Company pursuant to the immediately
preceding sentence, and all securities of holders who shall have requested such
inclusion in accordance herewith and who have not withdrawn such request prior
to the filing of such Registration Statement have been included in such a
Registration Statement which shall have become effective and such securities
shall have been effectively registered under the Securities Act, the Company
will have no further obligation to such holders under this Section 13(c) and the
Shares of such holders that have not been included previously in a Registration
Statement under this Section 13(c) will have no further registration rights
under this Agreement. In the event that (i) the managing underwriter for any
such offering advises the Company in writing that the inclusion of such
securities in the offering would be detrimental to the offering or (ii) in the
event that there is no managing underwriter, if, in the good faith judgment of
the Board of Directors of the Company, inclusion of the Shares in the
registration would be seriously detrimental to the Company, then, such
securities shall not be included in the Registration Statement. In the event
that securities requested to be included in an offering are not included in
accordance with the immediately preceding sentence, any notice given to holders
of Warrants and Shares hereunder with respect to such offering shall not be
counted against the limitation provided for in the second sentence of this
Section 13(c).

         (d) All fees, disbursements, and out-of-pocket expenses incurred in
connection with the filing of any Registration Statement under Section 13(c)
hereof and in complying with applicable securities and Blue Sky laws shall be
borne by the Company, provided, however, that any expenses of the holders of the
Warrants or the Shares, including but not limited to attorneys' fees and
discounts and commissions, shall be borne by such holders. The Company at its
expense will supply the holders of the Shares included in a Registration
Statement with copies of such Registration Statement and the prospectus or
offering circular included therein in such quantities as may be reasonably
requested by such holders.

         (e) Each holder of a Warrant or of Shares to be included in a
Registration Statement pursuant to this Section 13 agrees to reasonably
cooperate with the Company and to provide the Company on its request with all
information concerning such holder and his Warrants and Shares that may
reasonably be requested by the Company in order for the Company to perform its
obligations under this Section 13.


                                       12
<PAGE>   13
         Section 14. INDEMNIFICATION.

         (a) In the event of the filing of any Registration Statement with
respect to the Shares pursuant to Section 13 above, the Company agrees to
indemnify and hold harmless the holders of such Shares (for purposes of this
Section 14, references to any holder of Shares shall refer only to such holders
who have agreed to be bound by this Section 14), and each person who controls
such holders within the meaning of the Securities Act and such holders'
officers, directors, managers, members, partners, and principle equity holders
(collectively, "Indemnitees") against all losses, claims, damages, expenses and
liabilities, joint or several (which shall, for all purposes of this Agreement,
include, but not be limited to, all costs of defense and investigation and all
attorneys' fees and expenses), to which such Indemnitees may become subject,
under the Securities Act or otherwise, insofar as such losses, claims, damages,
expenses or liabilities (or actions in respect thereof) arise out of or are
based upon any untrue statement or alleged untrue statement of any material fact
contained in any such Registration Statement, or any related preliminary
prospectus, final prospectus, offering circular, notification or amendment or
supplement thereto, or arise out of or are based upon the omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein, in the light of the circumstances in
which they were made, not misleading; provided, however, that the Company will
not be liable in any such case to the extent that any such loss, claim, damage,
expenses, or liability arises out of or is based upon an untrue statement or
alleged untrue statement or omission or alleged omission made in such
Registration Statement, preliminary prospectus, final prospectus, offering
circular, notification or amendment or supplement thereto in reliance upon, and
in conformity with, written information furnished to the Company by any such
holder specifically for use in the preparation thereof and, provided further,
that the indemnity agreement provided in this Section 14(a) with respect to any
preliminary prospectus shall not inure to the benefit of any holder of Warrants
or Shares from whom the person asserting any losses, claims, damages,
liabilities or actions based upon any untrue statement or alleged untrue
statement of material fact or omission or alleged omission to state therein a
material fact purchased Warrants or Shares, if a copy of the prospectus in which
such untrue statement or alleged untrue statement or omission or alleged
omission was corrected had not been sent or given to such person within the time
required by the Securities Act and the rules and regulations thereunder, unless
such failure is the result of non-compliance by the Company with the last
sentence of Section 13(d) hereof. This indemnity will be in addition to any
liability which the Company may otherwise have.

         (b) Each holder of a Warrant and each holder of a Share agrees that he
will indemnify and hold harmless the Company, each other person referred to in
subparts (1), (2) and (3) of Section 11(a) of the Securities Act in respect of
the Registration Statement, each officer of the Company, and each person who
controls the Company within the meaning of the Securities Act, against any
losses, claims, damages or liabilities (which shall, for all purposes of this
Agreement, include, but not be limited to, all costs of defense and
investigation and all attorneys' fees) to which the Company or any such
director, officer or controlling person may become subject under the Securities
Act or otherwise, insofar as such losses, claims, damages or liabilities (or
actions


                                       13
<PAGE>   14
in respect thereof) arise out of or are based upon any untrue statement or
alleged untrue statement of any material fact contained in any such Registration
Statement, or any related preliminary prospectus, final prospectus, offering
circular, notification or amendment or supplement thereto, or arise out of or
are based upon the omission or alleged omission to state therein a material fact
required to be stated therein or necessary to make the statements therein not
misleading, but in each case only to the extent that such untrue statement or
alleged untrue statement or omission or alleged omission was made in such
Registration Statement, preliminary prospectus, final prospectus, offering
circular, notification or amendment or supplement thereto in reliance upon, and
in conformity with, written information furnished to the Company by such holder
specifically for use in the preparation thereof. This indemnity will be in
addition to any liability which the holder may otherwise have.

         (c) Promptly after receipt by an indemnified party under this Section
14 of notice of the commencement of any action, such indemnified party will, if
a claim in respect thereof is to be made against the indemnifying party under
this Section 14, notify the indemnifying party of the commencement thereof. No
indemnification provided for in this Section 14 shall be available to any party
who shall fail to give the notice to the extent the party to whom such notice
was not given was materially prejudiced by the failure to give the notice, but
the omission so to notify the indemnifying party will not relieve the
indemnifying party or parties from any liability which it may have to any
indemnified party for contribution otherwise than as to the particular item as
to which indemnification is then being sought solely pursuant to this Section
14. In case any such action is brought against any indemnified party, and it
notifies the indemnifying party of the commencement thereof, the indemnifying
party will be entitled to participate in, and, to the extent that it may wish,
jointly with any other indemnifying party similarly notified, reasonably assume
the defense thereof, subject to the provisions herein stated and after notice
from the indemnifying party to such indemnified party of its election so to
assume the defense thereof, the indemnifying party will not be liable to such
indemnified party under this Section 14 for any legal or other expenses
subsequently incurred by such indemnified party in connection with the defense
thereof other than reasonable costs of investigation unless the indemnifying
party shall not pursue the action to its final conclusion. The indemnified party
shall have the right to employ separate counsel in any such action and to
participate in the defense thereof, but the fees and expenses of such counsel
shall not be at the expense of the indemnifying party. No settlement of any
action against an indemnified party shall be made without the consent of the
indemnifying party, which shall not be unreasonably withheld in light of all
factors of importance to such indemnified party.

         Section 15. MERGER OR CONSOLIDATION OR CHANGE OF NAME OF WARRANT AGENT.

         (a) Any corporation into which the Warrant Agent may be merged or with
which it may be consolidated, or any corporation resulting from any merger or
consolidation to which the Warrant Agent shall be a party, or any corporation
succeeding to the corporate trust business of the Warrant Agent, shall be the
successor to the Warrant Agent hereunder without the execution or filing of any
paper or any further act on the part of any of the parties hereto, provided that
such


                                       14
<PAGE>   15
corporation would be eligible for appointment as a successor Warrant Agent under
the provisions of Section 18 of this Agreement. In case at the time such
successor to the Warrant Agent shall succeed to the agency created by this
Agreement and any of the Warrant certificates shall have been countersigned but
not delivered, any such successor to the Warrant Agent may adopt the
countersignature of the original Warrant Agent and deliver such Warrant
certificates so countersigned; and in case at that time any of the Warrant
certificates shall not have been countersigned, any successor to the Warrant
Agent may countersign such Warrant certificates either in the name of the
predecessor Warrant Agent or in the name of the successor Warrant Agent, and in
all such cases the Warrants represented by such Warrant certificates shall have
the full force provided in the Warrant certificates and in this Agreement. Any
such successor Warrant Agent shall promptly give notice of its succession as
Warrant Agent to the Company and to the registered holder of each Warrant
certificate.

         (b) If at any time the name of the Warrant Agent is changed and at such
time any of the Warrant certificates have been countersigned but not delivered,
the Warrant Agent may adopt the countersignature under its prior name and
deliver Warrant certificates so countersigned; and if at that time any of the
Warrant certificates have not been countersigned, the Warrant Agent may
countersign such Warrant certificates either in its prior name or in its changed
name; and in all such cases the Warrants represented by such Warrant
certificates will have the full force provided in the Warrant certificates and
in this Agreement.

         Section 16. CONCERNING THE WARRANT AGENT. The Company agrees to pay to
the Warrant Agent reasonable compensation for all services rendered by it
hereunder and, from time to time, on demand of the Warrant Agent, its reasonable
expenses and counsel fees and other disbursements incurred in the administration
and execution of this Agreement and the exercise and performance of its duties
hereunder. The Company also agrees to indemnify the Warrant Agent, and its
officers, agents and directors for, and to hold each of them harmless against,
any loss, liability, or expense incurred without negligence or willful
misconduct on the part of the Warrant Agent, for anything done or omitted by the
Warrant Agent or such indemnified party in connection with the acceptance or
administration of this Agreement or the exercise or performance of its duties
hereunder, including the costs and expenses of defending against any claim of
liability in the premises. The indemnification provided for hereunder shall
survive the expiration of the Warrant, the termination of this Agreement and the
resignation or removal of the Warrant Agent. The costs and expenses of enforcing
this right of indemnification shall also be paid by the Company.

         The Warrant Agent may conclusively rely upon and shall be protected by
the Company and shall incur no liability for, or in respect of any action taken,
suffered or omitted by it in connection with, its administration of this
Agreement or the exercise or performance of its duties hereunder in reliance
upon any Warrant certificate or certificate for the Common Stock or for other
securities of the Company, instrument of assignment or transfer, power of
attorney, endorsement, affidavit, letter, notice, direction, consent,
certificate, statement, or other paper or document believed by it to be genuine
and to be signed, executed and, where necessary, verified


                                       15
<PAGE>   16
or acknowledged, by the proper person or persons, or otherwise upon the advice
of counsel as set forth herein.

         Notwithstanding anything in this Agreement to the contrary, in no event
shall the Warrant Agent be liable for special, indirect or consequential loss or
damage of any kind whatsoever (including but not limited to lost profits), even
if the Warrant Agent has been advised of the likelihood of such loss or damage
and regardless of the form of the action.

         Section 17. DUTIES OF WARRANT AGENT. The Warrant Agent undertakes the
duties and obligations expressly imposed by this Agreement, and no implied
duties or obligations shall be read into this Agreement against the Warrant
Agent, upon the following terms and conditions, by all of which the Company and
the holders of Warrant certificates, by their acceptance thereof, shall be
bound:

         (a) Before the Warrant Agent acts or refrains from acting, 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 authorization and
protection to 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 Agreement the
Warrant Agent shall deem it necessary or desirable that any fact or factual
matter be proved or established by the Company prior to taking or suffering any
action hereunder, such fact or matter (unless other evidence in respect thereof
be herein specifically prescribed) may be deemed to be conclusively proved and
established by a certificate signed by any person believed in good faith by the
Warrant Agent to be one of the Chairman of the Board, the Chief Executive
Officer, the President, any Vice President, the Treasurer or the Secretary of
the Company and delivered to the Warrant Agent; and such certificate shall be
full authorization to the Warrant Agent for any action taken or suffered in good
faith by it under the provisions of this Agreement in reliance upon such
certificate.

         (c) The Warrant Agent shall be liable hereunder to the Company and any
other Person only for its own negligence, bad faith or wilful 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 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 is serving as an administrative agent and,
accordingly, shall not be under any responsibility in respect of the validity of
any provision of this Agreement or the execution and delivery hereof (except the
due execution hereof by the Warrant Agent) or in respect of 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


                                       16
<PAGE>   17
contained in this Agreement or in any Warrant certificate; nor shall it be
responsible for any change in the exercisability of the Warrant (including the
Warrant becoming void) or any adjustment in the terms of the Warrant (including
the manner, method or amount thereof) provided for herein, or the ascertaining
of the existence of facts that would require any such change or adjustment
(except with respect to the exercise of any Warrant evidenced by a Warrant
certificate after actual notice to the Warrant Agent that such change or
adjustment is required); 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 Agreement or any Warrant
certificate or as to whether any shares of Common stock will, when issued, be
validly authorized and issued, fully paid and nonassessable.

         (f) The Company agrees that it will perform, execute, 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 Agreement.

         (g) The Warrant Agent is hereby authorized and directed to accept
instructions with respect to the performance of its duties hereunder from any
person believed in good faith by the Warrant Agent to be one of the Chairman of
the Board, the Chief Executive Officer, the President, any Vice President, the
Treasurer, or the Secretary of the Company, and to apply to such officers for
advice or instructions in connection with its duties, and it shall not be liable
for any action taken or suffered by it in good faith in accordance with
instructions of any such officer of for any delay in acting while waiting for
those instructions.

                  Any application by the Warrant Agent for written instructions
from the Company may, at the option of the Warrant Agent, set forth in writing
any action proposed to be taken or omitted by the Warrant Agent under this
Agreement and the date on or after which such action shall be taken or such
omission shall be effective. The Warrant Agent shall not be liable for any
action taken by, or omission of, the Warrant Agent in accordance with a proposal
included in any such application on or after the date specified in such
application (which date shall not be less than ten Business Days after the date
any officer of the Company actually receives such application, unless any such
officer shall have consented in writing to an earlier date) unless, prior to
taking any such action (or the effective date in the case of an omission), the
Warrant Agent shall have received written instructions in response to such
application subject to the proposed action or omission and/or specifying the
action to be taken or omitted.

         (h) Subject to applicable law, the Warrant Agent and any stockholder,
director, officer or employee of the Warrant Agent may buy, sell or deal in any
of the Warrants or other securities of the Company or become pecuniarily
interested in any transaction in which the Company may be interested, or
contract with or lend money to the Company or otherwise act as fully and freely
as though it were not Warrant Agent under this Agreement. Nothing herein shall
preclude the Warrant Agent from acting in any other capacity for the Company or
for any other legal entity.


                                       17
<PAGE>   18
         (i) The Warrant Agent may execute and exercise any of the rights or
powers hereby vested in it or perform any duty hereunder either itself or by or
through its attorneys or agents, and the Warrant Agent shall not be answerable
or accountable for any act, default, neglect or misconduct of any such attorneys
or agents or for any loss to the Company resulting from any such act, default,
neglect or misconduct, provided that reasonable care was exercised in the
selection and continued employment thereof.

         (j) No provision of this Agreement shall require the Warrant Agent to
expend or risk its own funds or otherwise incur any financial liability in the
performance of any of its duties hereunder or in the exercise of its rights if
there shall be reasonable grounds for believing that repayment of such funds or
adequate indemnification against such risk or liability is not reasonably
assured to it.

         (k) The Warrant Agent shall not be required to take notice or be deemed
to have notice of any fact, event or determination (including, without
limitation, any dates or events defined in this Agreement) under this Agreement
unless and until the Warrant Agent shall be specifically notified in writing by
the Company of such fact, event or determination.

                  Section 18. CHANGE OF WARRANT AGENT. The Warrant Agent may
resign and be discharged from its duties under this Agreement by giving the
Company at least 30 days prior notice in writing, and by mailing notice in
writing to the registered holders at the expense of the Company at their
addresses appearing on the Warrant Register, of such resignation, at least 15
days prior to the date such resignation shall take effect and specifying a date
when such resignation shall take effect. The Warrant Agent may be removed by
like notice to the Warrant Agent from the Company and by like mailing of notice
to the registered holders of the Warrants. If the Warrant Agent resigns or is
removed or otherwise becomes incapable of acting, the Company shall appoint a
successor to the Warrant Agent. If the Company fails to make such appointment
within 30 days after such removal or after it has been notified in writing of
such resignation or incapacity by the resigning or incapacitated Warrant Agent
or by the registered holder of a Warrant (who shall, with such notice, submit
his Warrant certificate for inspection by the Company), then the Warrant Agent
or the registered holder of any Warrant may, at the expense of the Company,
apply to any court of competent jurisdiction for the appointment of a successor
to the Warrant Agent. Pending appointment of a successor to the Warrant Agent,
either by the Company or such a court, the Company shall carry out the duties of
the Warrant Agent. Any successor Warrant Agent, whether appointed by the Company
or by such a court, must be registered and otherwise authorized to serve as a
transfer agent pursuant to the Securities Exchange Act of 1934, as amended. If
at any time the Warrant Agent ceases to be eligible in accordance with the
provisions of this Section 18, it will resign immediately in the manner and with
the effect specified in this Section 18. After acceptance in writing of the
appointment, the successor Warrant Agent will be vested with the same powers,
rights, duties and responsibilities as if it had been originally named as
Warrant Agent without further act or deed; but the former Warrant Agent will
deliver and transfer to the successor Warrant Agent any property at the time
held by it hereunder, and execute and deliver any further assurance, conveyance,
act or deed


                                       18
<PAGE>   19
necessary for this purpose. Upon request of any successor Warrant Agent, the
Company will make, execute, acknowledge and deliver any and all instruments in
writing for more fully and effectually vesting in and confirming to such
successor Warrant Agent all such powers, rights, duties and responsibilities.
Failure to file or mail any notice provided in this Section 18, however, or any
defect therein, will not affect the legality or validity of the resignation or
removal of the Warrant Agent or the appointment of the successor Warrant Agent,
as the case may be.

         Section 19. IDENTITY OF TRANSFER AGENT. Following the appointment of
any transfer agent for the Common Stock or of any subsequent transfer agent for
shares of the Common Stock or other shares of the Company's capital stock
issuable upon the exercise of the rights of purchase represented by the
Warrants, the Company will file with the Warrant Agent a statement setting forth
the name and address of such transfer agent.

         Section 20. NOTICES. Notices or demands authorized by this 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
registered or certified mail, addressed (until another address is filed in
writing with the Warrant Agent) as follows (and shall be deemed given upon
receipt):

                           Ugly Duckling Corporation
                           2525 East Camelback Road
                           Suite 1150
                           Phoenix, Arizona 85016
                           Attention: Steven P. Johnson, Senior Vice President,
                                      General Counsel and Secretary

                           With a copy to:

                           Steven D. Pidgeon
                           Snell & Wilmer L.L.P.
                           One Arizona Center
                           Phoenix, Arizona 85004-0001


                                       19
<PAGE>   20
Notices or demands authorized by this Agreement to be given or made by the
Company or by the holder of any Warrant certificate to or on the Warrant Agent
shall be sent by registered or certified mail, addressed (until another address
is filed in writing with the Company) as follows (and shall be deemed given upon
receipt):

                           Harris Trust Company of California
                           601 South Figueroa
                           49th Floor
                           Los Angeles, CA 90017
                           Attention: Neil Rosso, Corporate Trust

Notices or demands authorized by this Agreement to be given or made by the
Company or the Warrant Agent to the holder of any Warrant certificate shall be
sufficiently given or made if sent by first class mail, postage prepaid,
addressed to such holder at the address of such holder as shown in the Warrant
Register. The Company shall deliver a copy of any notice or demand it delivers
to the holder of any Warrant certificate to the Warrant Agent.

         Section 21. SUPPLEMENTS AND AMENDMENTS. The Company and the Warrant
Agent may from time to time supplement or amend this Agreement without the
approval of any holders of Warrants in order to cure any ambiguity or to correct
or supplement any provision contained herein which may be defective or
inconsistent with any other provision herein, or to make any other provisions in
regard to matters or questions arising hereunder which the Company and the
Warrant Agent may deem necessary or desirable and which shall not be
inconsistent with the provisions of the Warrants, or which shall not adversely
affect the interests of the holders of Warrants (including reducing the Warrant
Price or extending the redemption or expiration date). In any situation in which
this Agreement cannot be amended pursuant to the next sentence above, this
Agreement may be amended by the Company, the Warrant Agent and the holder or
holders of a majority of the outstanding Warrants representing a majority of the
shares of Common Stock underlying such Warrants; provided, however, that without
the consent of each holder of a Warrant, there can be no increase of the Warrant
Price or reduction of the exercise period for such holder's Warrants and
provided, further, that no such supplement or amendment may affect the rights or
duties of the Warrant Agent under this Agreement without the written consent of
the Warrant Agent. Notwithstanding anything in this Agreement to the contrary,
no supplement or amendment that changes the rights and duties of the Warrant
Agent under this Agreement shall be effective against the Warrant Agent without
the execution of such supplement or amendment by the Warrant Agent.

         Section 22. SUCCESSORS. All the covenants and provisions of this
Agreement by or for the benefit of the Company, or the Warrant Agent or the
registered holders of the Warrants will bind and inure to the benefit of their
respective successors and assigns hereunder.

         Section 23. GOVERNING LAW. This Agreement will be deemed to be a
contract made under the laws of the State of Arizona and for all purposes will
be construed in accordance with


                                       20
<PAGE>   21
the laws of said State, except as to Sections 16, 17 and 21, which shall be
governed by and construed in accordance with the laws of the State of Illinois.
Each holder of a Warrant by its acceptance thereof agrees to submit to the
jurisdiction of a court of competent jurisdiction in the State of Arizona, but
to the State of Illinois as to Sections 16, 17 and 21, for the purpose of
resolving any disputes arising with respect to the rights and obligations of the
Warrant Agent.

         Section 24. BENEFITS OF THIS AGREEMENT. Nothing in this Agreement will
be construed to give to any person or corporation other than the Company, the
Warrant Agent and the registered holders of the Warrants any legal or equitable
right, remedy or claim under this Agreement. This Agreement is for the sole and
exclusive benefit of the Company, the Warrant Agent and the registered holders
of the Warrants.

         Section 25. COUNTERPARTS. This Agreement may be executed in
counterparts and each of such counterparts will for all purposes be deemed to be
an original, and all such counterparts will together constitute but one and the
same instrument.

         Section 26. DESCRIPTIVE HEADINGS. The descriptive headings of the
several Sections of this Agreement are inserted for convenience only and do not
control or affect the meaning or construction of any of the provisions hereof.

         IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed, as of the day and year first above written.

                                    UGLY DUCKLING CORPORATION

                                    By: /s/ Steven P. Johnson            
                                    ------------------------------------    
                                    Name: Steven P. Johnson              
                                    ------------------------------------
                                    Its: Sr. V.P. & Secretary            
                                    ------------------------------------


                                    RELIANCE ACCEPTANCE GROUP, INC.

                                    By: /s/ James T. Moran               
                                    ------------------------------------
                                    Name: James T. Moran                 
                                    ------------------------------------
                                    Its: President & CEO                 
                                    ------------------------------------




                                       21
<PAGE>   22
                                    HARRIS TRUST COMPANY
                                    OF CALIFORNIA, AS WARRANT AGENT

                                    By: /s/ Neil T. Rosso
                                        ---------------------------------
                                    Name: Neil T. Rosso
                                          -------------------------------
                                    Its: Asst. V.P.
                                         --------------------------------

                                       22
<PAGE>   23
Warrant No. ___

                                    EXHIBIT A

               WARRANT TO PURCHASE ________ SHARES OF COMMON STOCK

                              VOID AFTER 5:00 P.M.,
                  NEW YORK CITY TIME, ON ___________ ___, _____

                            UGLY DUCKLING CORPORATION

         This certifies that, for value received ________________________, the
registered holder hereof or assigns (the "Holder"), is entitled to purchase from
UGLY DUCKLING CORPORATION, a Delaware corporation (the "Company"), at any time
after ________ ___, ______ and before 5:00 p.m., New York City time, on
_______________ ___, _____ at the purchase price per share of $___ (the "Warrant
Price"), the number of shares of Common Stock, par value $0.001 per share, of
the Company set forth above (the "Shares"). The number of shares of Common Stock
purchasable upon exercise of the Warrant evidenced hereby and the Warrant Price
is subject to adjustment from time to time as set forth in the Warrant Agreement
referred to below.

         The Warrants evidenced hereby may be exercised during the period
referred to above, in whole or in part, by presentation of this Warrant
certificate with the Purchase Form attached hereto duly executed and guaranteed
and simultaneous payment of the Warrant Price (as defined in the Warrant
Agreement and subject to adjustment as provided therein) at the principal office
in Los Angeles, California, of Harris Trust Company of California (the "Warrant
Agent"). Payment of such price may be made at the option of the Holder in cash
or by certified check or bank draft or pursuant to a cashless exercise, all as
provided in the Warrant Agreement.

         The Warrants evidenced hereby are part of a duly authorized issue of
Warrants and are issued under and in accordance with the Warrant Agreement dated
as of February 9, 1998, between the Company and the Warrant Agent, and are
subject to the terms and provisions contained in such Warrant Agreement, which
Warrant Agreement is hereby incorporated by reference herein and made a part
hereof and is hereby referred to for a description of the rights, limitations,
duties and indemnities thereunder of the Company and the Holder of the Warrants,
and to all of which the Holder of this Warrant certificate by acceptance hereof
consents. A copy of the Warrant Agreement may be obtained for inspection by the
Holder hereof upon written request to the Warrant Agent.

         Upon any partial exercise of the Warrants evidenced hereby, there will
be issued to the Holder a new Warrant certificate in respect of the Shares
evidenced hereby that have not been exercised. This Warrant certificate may be
exchanged at the office of the Warrant Agent by


                                        1
<PAGE>   24
surrender of this Warrant certificate properly endorsed either separately or in
combination with one or more other Warrants for one or more new Warrants to
purchase the same aggregate number of Shares as evidenced by the Warrant or
Warrants exchanged. No fractional Shares will be issued upon the exercise of
rights to purchase hereunder, but the Company will pay the cash value of any
fraction upon the exercise of one or more Warrants, as provided in the Warrant
Agreement.

         The Warrant Price and the number of shares of Common Stock issuable
upon exercise of this Warrant is subject to adjustment as provided in Section 9
of the Warrant Agreement. The Warrant Agreement may be amended by the Company
and the Warrant Agent in certain limited events and by the holder or holders of
a majority of the outstanding Warrants representing a majority of the shares of
Common Stock underlying such Warrants; provided that without the consent of each
holder of a Warrant certain specified changes cannot be made to such holder's
Warrants and no amendment may affect the rights and duties of the Warrant Agent
without the consent of the Warrant Agent. Pursuant to the Warrant Agreement, by
acceptance of a Warrant, each holder consents to the jurisdiction of a court of
competent jurisdiction in the State of Arizona for the purpose of resolving any
disputes arising with respect to the Warrants or the Warrant Agreement.

         The Holder hereof may be treated by the Company, the Warrant Agent and
all other persons dealing with this Warrant certificate as the absolute owner
hereof for all purposes and as the person entitled to exercise the rights
represented hereby, any notice to the contrary notwithstanding, and until any
transfer is entered on such books, the Company may treat the Holder hereof as
the owner for all purposes. Notices and demands to be given to the Company or
the Warrant Agent must be given by certified or registered mail at the addresses
provided in the Warrant Agreement.

         All terms used in the Warrant Certificate that are defined in the
Warrant Agreement shall have the respective meanings ascribed to such terms in
the Warrant Agreement.

Dated:________________              UGLY DUCKLING CORPORATION

                                    By:__________________________________
                                       President

ATTEST:

_____________________________
Secretary


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<PAGE>   25
                                      This is one of the Warrants referred to 
                                      in the within mentioned Warrant Agreement.

                                      HARRIS TRUST COMPANY
                                      OF CALIFORNIA

                                   By:__________________________________
                                      Authorized Representative


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<PAGE>   26
                            UGLY DUCKLING CORPORATION
                                  PURCHASE FORM

                                Mailing Address:
                            UGLY DUCKLING CORPORATION
                            2525 East Camelback Road
                                   Suite 1150
                             Phoenix, Arizona 85016

         The undersigned hereby irrevocably elects to exercise the right of
purchase represented by the within Warrant certificate for, and to purchase
thereunder, _____________Shares of Common Stock provided for therein, and
requests that certificates for such Shares be issued in the name of:
________________________________________________________________________________
________________________________________________________________________________
(Please Print or Type Name, Address and Social Security Number)

and that such certificates be delivered to ____________________________________
whose address is _______________________________________________________________
and, if said number of Shares shall not be all the Shares purchasable hereunder,
that a new Warrant certificate for the balance of the Shares purchasable under
the within Warrant certificate be registered in the name of the undersigned
Holder or his or her Assignee as below indicated and delivered to the address
stated below.

                                                     Dated:_____________________
Name of Holder or Assignee:

________________________________________________________________________________
(Please Print)

Address:________________________________________________________________________
________________________________________________________________________________

Signature:

__________________________________
NOTE: The above signature must correspond with the name as it appears upon the
face of the within Warrant certificate in every particular, without alteration
or enlargement or any change whatever, unless these Warrants have been assigned.

Signature Guaranteed:

__________________________________
THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR
INSTITUTION (Banks, Stock Brokers, Savings and Loan Association, and Credit
Unions) WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM
PURSUANT TO S.E.C. RULE 17Ad-15.
<PAGE>   27
                                   ASSIGNMENT

                 (To be signed only upon assignment of Warrants)

  FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers unto

_______________________________________________________________________________
          (Name and Address of Assignee Must Be Printed or Typewritten)

_______________________________________________________________________________

______________ Warrants, hereby irrevocably constituting and appointing _______
Attorney to transfer said Warrants on the books of the Company, with full power
of substitution in the premises.

Dated:_______________________


                                          _____________________________________
                                             Signature of Registered Holder

                                   Note: The signature on this assignment must
                                         correspond with the name as it appears
                                         upon the face of the within Warrant 
                                         certificate in every particular, 
                                         without alteration or enlargement or 
                                         any change whatever.

Signature Guaranteed:


______________________________
THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR
INSTITUTION (Banks, Stock Brokers, Savings and Loan Association, and Credit
Unions) WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM
PURSUANT TO S.E.C. RULE 17Ad-15.


                                        5
<PAGE>   28
                                    EXHIBIT B


         The number of Warrants set forth below will be issuable upon
satisfaction of the conditions set forth below and will be issued as soon as
practicable after such conditions have been satisfied.

         (1) 50,000 Warrants to be issued as of February 9, 1998, subject to the
receipt by the Company, Champion Acceptance Corporation ("CAC"), or another
subsidiary or affiliate of the Company of $1.3 million in proceeds realized by
Reliance from the sale of the pool of Charged-Off Receivables existing as of the
Petition Date;

         (2) an additional 100,000 Warrants upon the receipt by the Company,
CAC, or another subsidiary or affiliate of the Company of $4.7 million of
post-Bank Claim Satisfaction Date Cash Flow from the Receivables Portfolio and
in the event that less than $4.7 million of such post-Bank Claim Satisfaction
Date Cash Flow is received, a number of Warrants corresponding pro-rata to the
proportionate amount of such post-Bank Claim Satisfaction Date Cash Flow
received, in increments of not less than $940,000 to be issued as of the last
day of each quarter(1); and

         (3) an additional 75,000 Warrants for every $1 million actually
received by the Company, CAC, or another subsidiary or affiliate of the Company
on account of its Incentive Fee.

         For purposes of the above, the capitalized terms shall have the
meanings ascribed to them in Reliance's Joint Plan of Reorganization dated
February 9, 1998, as amended.


----------
         (1) The following is an example of the issuance of Warrants pursuant to
paragraph (2) above.

         Assume $940,000 of post-Bank Claim Satisfaction Date Cash Flow has been
received by the Company from the Receivables Portfolio by the end of the first
quarter following the Petition Date. The Company must issue 20,000 Warrants to
Reliance [($940,000 / $4,700,000) x 100,000] = 20,000.

         Assume an additional $900,000 is received by the end of the second
quarter following the Petition Date, for a total of $1,840,000. No additional
Warrants would be required to be issued because receipts had not reached the
second increment of at least $940,000.

         Assume an additional $500,000 (in addition to the $1,840,000 received
previously) is received by the end of the third quarter following the Petition
Date, for a total of $2,340,000. The Company must issue 29,787 additional
Warrants to Reliance [($2,340,000 / $4,700,000) x 100,000] = 49,787.23, which is
then rounded to 49,787, less the 20,000 Warrants previously issued = 29,787
additional Warrants.


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