<PAGE>   1
                                                                    EXHIBIT 10.2


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

                           CERTIFICATE OF DESIGNATION
                                       OF
                              STARBASE CORPORATION

                     Pursuant to Section 151 of the General
                    Corporation Law of the State of Delaware
                     ---------------------------------------


                            SERIES H PREFERRED STOCK


     StarBase Corporation, a Delaware corporation (the "Corporation"), hereby
certifies that the following resolution has been duly adopted by the Board of
Directors of the Corporation:

     RESOLVED, that pursuant to the authority expressly granted to and vested in
the Board of Directors of the Corporation (the "Board") by the provisions of the
Restated Certificate of Incorporation of the Corporation (the "Certificate of
Incorporation"), there hereby is created, out of the 10,000,000 shares of
Preferred Stock, par value $0.01 per share, of the Corporation authorized in
Article 4 of the Certificate of Incorporation (the "Preferred Stock"), a series
of the Preferred Stock of the Corporation consisting of three thousand five
hundred (3,500) shares, which series shall have the following powers,
designations, preferences and relative, participating, optional and other
rights, and the following qualifications, limitations and restrictions:

     1.   Designation and Amount. This series of Preferred Stock shall be
designated "Series H Preferred Stock" and the authorized number of shares
constituting such series shall be three thousand five hundred (3,500). The par
value of the Series H Preferred Stock shall be $0.01 per share.

     2.   Dividend Rights of Series H Preferred Stock. The holders of the Series
H Preferred Stock shall not be entitled to receive any dividends.

     3.   Preference on Liquidation.

          (a)  In the event of any liquidation, dissolution, or winding up of
the Corporation, either voluntary or involuntary, distributions to the
stockholders of the Corporation shall be made in the following manner:

               (i)  The holders of Series H Preferred Stock shall be entitled to
receive, prior and in preference to any distribution of any of the assets or
surplus funds to the holders of the Corporation's common stock, par value $0.01
per share (the "Common Stock") or any other 



<PAGE>   2

class or series of stock of this Corporation by reason of their ownership of
such stock, an amount for each share of Series H Preferred Stock then held by
them, equal to $1,000, appropriately adjusted for any combinations,
consolidations, stock distributions or stock dividends with respect to such
shares (hereinafter such amount shall be referred to as the "Series H Preference
Amount"). If upon occurrence of such event of liquidation, dissolution or
winding up, the assets and property legally available to be distributed among
the holders of the Series H Preferred Stock shall be insufficient to permit the
payment to such holders of the Series H Preference Amount, then the entire
assets and property of the Corporation legally available for distribution shall
be distributed ratably among the holders of the Series H Preferred Stock
together with the holders of any other series of Preferred Stock ranking on
parity with the Series H Preferred Stock.

               (ii) After payment has been made to the holders of the Series H
Preferred Stock of the full amounts to which they shall be entitled pursuant to
paragraph 3(a)(i) above, all remaining assets available for distribution, if
any, shall be distributed, ratably among the holders of the Common Stock based
upon the number of shares of Common Stock then held.

          (b)  For purposes of this paragraph 3, a merger or consolidation of
the Corporation with or into any other corporation or corporations, or the
merger of any other corporation or corporations into the Corporation, in which
consolidation or merger the stockholders of the Corporation receive
distributions in cash or securities of another corporation or corporations as a
result of such consolidation or merger, or a sale of all or substantially all of
the assets of the Corporation, shall be treated as a liquidation, dissolution or
winding up of the Corporation. The valuation of any securities or other property
other than cash received by the Corporation in any transaction covered by this
subparagraph 3(b) shall be computed at the fair value thereof at the time of
receipt as determined in good faith by the Board of Directors.

          (c)  The holders of Series H Preferred Stock shall have no priority or
preference with respect to distributions made by the Corporation in connection
with the repurchase of shares of Common Stock issued to or held by employees,
directors or consultants upon termination of their employment or services
pursuant to agreements providing for the right of said repurchase between the
Corporation and such persons.

     4.   Voting Rights. Except as otherwise provided by law, the holders of the
Series H Preferred Stock shall not be entitled to vote upon any matter relating
to the business or affairs of the Corporation or for any other purpose.

     5.   Conversion Rights. The holders of Series H Preferred Stock shall have
conversion rights as follows:

          (a)  The holders will deliver to the Corporation a notice of
conversion (a "Notice of Conversion") and the original shares of Series H
Preferred Stock to be converted within three business days from the Conversion
Date (as hereinafter defined). A Notice of Conversion may only be served on a
business day between the hours of 7:00 a.m., and 5:00 p.m., 



                                      -2-
<PAGE>   3

Pacific time, and shall be deemed delivered upon facsimile receipt by the
Corporation with such time period or the next business day if served after 5:00
p.m., Pacific time. The Corporation will then deliver to the holders within
three business days of facsimile receipt (provided that the original shares of
Series H Preferred Stock were delivered to the Corporation within three business
days of the Conversion Date) of the holder's Notice of Conversion the
appropriate number of shares of Common Stock. If the Corporation fails to
deliver the Common Stock within five business days of facsimile receipt
(provided that the original shares of Series H Preferred Stock were delivered to
the Corporation within three business days of the Conversion Date) of the
holder's Notice of Conversion, the Corporation will be liable for liquidated
damages, as follows: in the event that the Common Stock issuable upon conversion
of the Series H Preferred Stock is not delivered within five (5) business days
after the Conversion Date, the Corporation shall pay to the holders, in
immediately available funds, upon demand, as liquidated damages for such failure
and not as a penalty, for each $100,000 principal amount of Series H Preferred
Stock sought to be converted, $500 for each of the first ten (10) calendar days
and $1,000 per calendar day thereafter that the shares of Common Stock issuable
upon such conversion are not delivered, which liquidated damages shall run from
the sixth (6th) business day after the Conversion Date up until the time that
either the Notice of Conversion is revoked or the Common Stock has been
delivered, at which time liquidated damages shall cease. Any and all payments
required pursuant to this paragraph shall be payable only in cash immediately.
Payment of the aforementioned liquidated damages shall not relieve the Company
of its obligation to deliver the shares of Common Stock due upon conversion of
the Series H Preferred Stock. For purposes of this Certificate of Designation,
"Conversion Date" shall mean the date on which the holders give notice of
conversion by facsimile to the Corporation.

          (b)  A holder of Series H Preferred Stock may convert up to one third
of its shares of Series H Preferred Stock into shares of Common Stock at any
time after 120 days from the date of issuance of the first tranche of Series H
Preferred Stock (the "First Conversion Date"). A holder may convert an
additional one third of the shares of Series H Preferred Stock purchased 30 and
60 days after the First Conversion Date. Notwithstanding anything in the
foregoing to the contrary, if at any time after the First Conversion Date, the
Common Stock of the Corporation has traded for five (5) consecutive trading days
at a closing bid price that is greater than or equal to $3.00, then a holder may
convert all of its outstanding shares of Series H Preferred Stock without regard
to the restrictions on conversion set forth in this clause (b).

          (c)  The shares of Series H Preferred Stock may be converted into
shares of Common Stock at a price to the lesser of: (a) 110% of the average of
the closing bid prices of the Common Stock for the five consecutive day trading
period ending on the trading date immediately preceding the issuance date of the
shares of Series H Preferred Stock (the "Closing Price") or (b) 100% of the
"Market Price", where the Market Price is defined as the average of the two (2)
lowest closing bid prices of the Common Stock over the thirty (30) consecutive
trading days immediately preceding the Conversion Date (the "Conversion Price").



                                      -3-
<PAGE>   4

          (d)  Each share of Series H Preferred Stock shall be convertible, at
the option of the holder thereof, at any time after the date of issuance of such
share, at the office of the Corporation or any transfer agent for the Series H
Preferred Stock, into Common Stock as more fully described below. The number of
shares of fully paid and nonassessable Common Stock into which each share of
Series H Preferred Stock may be converted shall be determined by dividing $1000
by the Conversion Price in effect at the time of conversion, subject to
adjustment as provided in Paragraph 6 below.

          (e)  Each share of Series H Preferred Stock shall automatically be
converted into shares of Common Stock utilizing the then effective Conversion
Price for each such share upon the first to occur of the following events: (i)
at the Corporation's option, if the closing bid price of the Company's Common
Stock, as reported by Bloomberg, L.P., on a daily basis averages at least
$US5.00 for a period of 20 consecutive trading days assuming the registration
statement is effective and all conversion restrictions have lapsed for at least
30 calendar days; or (ii) the second anniversary of the effective date of the
registration of the shares of Common Stock issuable upon conversion of the
Series H Preferred Stock (in such case the second anniversary shall be deemed a
Conversion Date). In the event of clause (i) above, the Corporation must notify
each holder of Series H Preferred Stock in writing within ten (10) business days
after such 20 consecutive trading day period that such stock is to be converted
and the date such holder receives the notice shall be deemed a Conversion Date.

          (f)  No fractional shares of Common Stock shall be issued upon
conversion of Series H Preferred Stock. In lieu of any fractional shares to
which the holder would otherwise be entitled, the Corporation shall pay cash
equal to such fraction multiplied by the closing bid price of the Common Stock
on the Conversion Date. In the event of an automatic conversion pursuant to
subparagraph 5(e), the outstanding shares of all Series H Preferred Stock shall
be converted automatically and the original shares of Series H Preferred Stock
and the shares of Common Stock will be delivered in accordance with subparagraph
5(a). In the event that a holder notifies the Corporation that its certificates
evidencing its shares of Series H Preferred Stock have been lost, stolen or
destroyed, the holder shall execute an agreement satisfactory to the Corporation
to indemnify the Corporation from any loss incurred in connection with such
certificates.

          (g)  The Corporation shall, within three business days after a
Conversion Date issue and deliver at such office to such holder of Series H
Preferred Stock, a certificate or certificates for the number of shares of
Common Stock to which the holder shall be entitled as aforesaid and a check
payable to the holder, or order, in the amount of any cash amounts payable as
the result of a conversion into fractional shares of Common Stock, and a
certificate for any shares of Series H Preferred Stock not so converted. Such
conversion shall be deemed to have been made immediately prior to the close of
business on the Conversion Date, or in the case of automatic conversion under
clause (i) of subparagraph 5(e), the date notice is received by the holders of
the Series H Preferred Stock or under clause (ii) of subparagraph 5(e) on the
date of the event causing such automatic conversion, and the person or persons
entitled to receive the 



                                      -4-
<PAGE>   5

shares of Common Stock issuable upon such conversion shall be treated for all
purposes as the record holder or holders of such shares of Common Stock on such
date.

          (h)  In the event of any taking by this Corporation of a record of the
holders of any class of shares of securities for the purpose of determining the
holders thereof who are entitled to receive any dividend (other than a cash
dividend) or other distribution, any right to subscribe for, purchase or
otherwise acquire any shares of stock of any class or any other securities or
property, or to receive any other right, this Corporation shall mail to each
holder of Series H Preferred Stock, at least 20 days prior to the date specified
therein, a notice specifying the date on which any such record is to be taken
for the purpose of such dividend, distribution or right, and the amount and
character of such dividend, distribution or right.

          (i)  Upon any conversion of Series H Preferred Stock pursuant to this
paragraph 5, the shares of Series H Preferred Stock which are converted shall
not be reissued. Upon conversion of all of the then outstanding Series H
Preferred Stock pursuant to this paragraph 5 and upon the taking of any action
required by law, all matters set forth in this Certificate of Designation shall
be eliminated from the Certificate of Incorporation, shares of Series H
Preferred Stock shall not be deemed outstanding for any purpose whatsoever and
all such shares shall revert to the status of authorized and unissued shares of
Preferred Stock.

          (j)  Unless otherwise set forth herein, any notices required by the
provisions of this paragraph 5 to be given to the holders of shares of Series H
Preferred Stock shall be deemed given if deposited in the United States mail,
first class, postage prepaid and addressed to each holder of record at its
address appearing on the books of the Corporation.

          (k)  The Corporation will notify in writing each of the holders of
Series H Preferred Stock when the number of shares of Common Stock issuable upon
conversion of Series H Preferred Stock equals 17%, 18%, 19% and 20% of the
issued and outstanding shares of the Common Stock. If the Corporation receives a
Notice of Conversion which would result in the number of shares of Common Stock
issuable upon conversion of Series H Preferred Stock in excess of 20%, the
Corporation will notify the holders in writing prior to the end of the trading
day if the Notice of Conversion was received on or before 2:00 p.m., New York
time, or prior to the opening of trading on the next trading day if the Notice
of Conversion was received after 2:00 p.m., New York time. If conversion under
the Notice of Conversion would result in the issuance of more than 20% of the
issued and outstanding shares of the Common Stock, the holders may elect to
rescind that portion of the Notice of Conversion which would result in the
issuance of more that 20% of the issued and outstanding shares of the Common
Stock, while reserving their rights to serve a Notice of Conversion at a later
date.

     6.   Adjustments to Conversion Price.

          (a)  In the event the Corporation at any time or from time to time
effects a subdivision or combination of its outstanding Common Stock into a
greater or lesser number of 



                                      -5-
<PAGE>   6

shares without a proportionate and corresponding subdivision or combination of
its outstanding Series H Preferred Stock, then and in each such event the
Conversion Price shall be decreased or increased proportionately.

          (b)  In the event the Corporation at any time or from time to time
shall make or issue, or fix a record date for the determination of holders of
Common Stock entitled to receive, a dividend or other distribution payable in
additional shares of Common Stock or other securities or rights (hereinafter
referred to as "Common Stock Equivalents") convertible into or entitling the
holder thereof to receive additional shares of Common Stock without payment of
any consideration by such holder for such Common Stock Equivalents or the
additional shares of Common Stock, then and in each such event the maximum
number of shares (as set forth in the instrument relating thereto without regard
to any provisions contained therein for a subsequent adjustment of such number)
of Common Stock issuable in payment of such dividend or distribution or upon
conversion or exercise of such Common Stock Equivalents shall be deemed to be
issued and outstanding as of the time of such issuance or, in the event such a
record date shall have been fixed, as of the close of business on such record
date. In each such event, the Conversion Price shall be proportionately
decreased as of the time of such issuance or, in the event such a record date
shall have been fixed, as of the close of business on such record date.

          (c)  In case of any merger (other than a merger in which the
Corporation is not the continuing or surviving entity) or any reclassification
of the Common Stock of the Corporation, each share of the Series H Preferred
Stock shall thereafter be entitled to receive such additional number of shares
of stock or other securities or property to which a holder of the number of
shares of Common Stock issuable upon conversion of a share of Series H Preferred
Stock immediately prior to such merger or reclassification would have been
entitled upon such merger or reclassification. In any such case, appropriate
adjustment (as determined by the Board in good faith) shall be made in the
application of the provisions herein set forth with respect to the rights and
interests thereafter of the holders of Series H Preferred Stock, such that the
provisions set forth herein shall thereafter be applicable, as nearly as
reasonably may be, in relation to any share of stock or other property
thereafter issuable upon conversion.

          (d)  The Corporation shall at all times reserve and keep available out
of its authorized but unissued Common Stock, solely for the purpose of effecting
the conversion of Series H Preferred Stock, the full number of shares of Common
Stock deliverable upon the conversion of all Series H Preferred Stock from time
to time outstanding. The Corporation shall from time to time (subject to
obtaining necessary director and stockholder authorizations), in accordance with
the laws of the State of Delaware, increase the authorized amount of its Common
Stock if at any time the authorized number of shares of Common Stock remaining
unissued shall not be sufficient to permit the conversion of all of the shares
of Series H Preferred Stock at the time outstanding.

     7.   Ranking. The Series H Preferred Stock shall, with respect to rights on
liquidation, winding up and dissolution, (i) rank senior to any of the Common
Stock and any other class or 



                                      -6-
<PAGE>   7

series of stock of the Corporation which by its terms shall rank junior to the
Series H Preferred Stock, (ii) rank junior to any other class or series of stock
of the Corporation which by its terms shall rank senior to the Series H
Preferred Stock, and (iii) rank on a parity with any other class or series of
stock of the Corporation which by its terms shall rank on a parity with the
Series H Preferred Stock. No approval of the holders of Series H Preferred Stock
shall be required for the authorization or issuance of any shares of any class
or series of stock of the Corporation, whether ranking senior to, junior to or
on a parity with the Series H Preferred Stock.

     8.   Corporation's Redemption Option. The Corporation may redeem all or a
portion of the Series H Convertible Preferred Stock upon five (5) business days
prior written notice to the holders of the Series H Preferred Stock (the
"Redemption Notice") at a price per share of Series H Preferred Stock (the
"Redemption Price") equal to the greater of (i) 120% of the Series H Preference
Amount; and (ii) the product of (A) the Conversion Price and (B) the closing bid
price of the Common Stock on the trading date immediately preceding the date of
the Redemption Notice; provided, that if a holder has delivered a notice of
conversion to the Corporation or delivers a notice of conversion within two (2)
business days after receipt of the Redemption Notice, the shares of Series H
Convertible Preferred Stock designated to be converted may not be redeemed by
the Corporation. The Corporation shall deliver the Redemption Price in
immediately available funds to the holder(s) within five (5) business days after
the Corporation has delivered the Redemption Notice; provided, that if the
Corporation fails to pay the Redemption Price within such five (5) business-day
period, the Redemption Notice shall be null and void. The Corporation may not
serve a Redemption Notice unless it has immediately available funds specifically
allotted as the Redemption Price as set forth in such notice. The Redemption
Notice may only be served on a business day between the hours of 9:00 a.m. and
5:00 p.m. New York time, and shall be deemed delivered upon facsimile receipt by
the holders of the Series H Preferred Stock within such time period or such
immediately subsequent business day if served after such hours. Redemptions must
be pro rata amongst the holders of Series H Preferred Stock, if fewer than all
of the outstanding shares of Series H Preferred Stock are being redeemed. The
Redemption Notice shall set forth (i) the Redemption Price (including
calculations) and (ii) the number of shares of Series H Preferred Stock being
redeemed. The Redemption Price shall be adjusted proportionately upon any
adjustment to the Conversion Price as provided herein and in the event of any
stock split, stock dividend, combination of shares or similar event. If the
Company fails to comply with the redemption provisions on two separate
occasions, it shall lose its right to serve a Redemption Notice in the future.

     9.   Limitation on Number of Conversion Shares.

          (a)  Notwithstanding any other provision herein, the Corporation shall
not be obligated to issue any shares of Common Stock upon conversion of the
Series H Preferred Stock if the issuance of such shares of Common Stock would
exceed that number of shares of Common Stock which the Corporation may issue
upon conversion of the Series H Preferred Stock (the "Exchange Cap") without
breaching the Corporation's obligations under the rules or regulations of The
Nasdaq Stock Market, Inc., except that such limitation shall not apply in the



                                      -7-
<PAGE>   8

event that the Corporation (a) obtains the approval of its stockholders as
required by applicable rules of The Nasdaq Stock Market, Inc. for issuances of
Common Stock in excess of such amount or (b) obtains a written opinion from
outside counsel to the Corporation that such approval is not required, which
opinion shall be reasonably satisfactory to the holders of a majority of the
shares of Series H Preferred Stock then outstanding; provided, however, that
notwithstanding anything herein to the contrary, the Corporation, will issue (x)
such number of shares of Common Stock issuable upon conversion of the Series H
Preferred Stock at the then current Conversion Price up to the Exchange Cap, (y)
such number of shares of Common Stock issuable upon conversion of the remaining
outstanding Series H Preferred Stock at the closing bid price as reported by
Bloomberg, L.P. on the date preceding the applicable Conversion Date, and (z)
warrants to purchase such number of shares of Common Stock based on a ratio of
200,000 shares for each $1,000,000 of Series H Preferred Stock which cannot be
converted at the then current Conversion Price, which warrants shall have an
exercise price equal to the then current market price and an exercise period of
eighteen months from the date of issuance. Until such approval or written
opinion is obtained, no holder of Series H Preferred Stock pursuant to the
Securities Purchase Agreement shall be issued, upon conversion of shares of
Series H Preferred Stock, shares of Common Stock in an amount greater than the
product of (i) the Exchange Cap amount multiplied by (ii) a fraction, the
numerator of which is the number of shares of Series H Preferred Stock issued to
such holder pursuant to the Securities Purchase Agreement and the denominator of
which is the aggregate amount of all the shares of Series H Preferred Stock
issued to the holders pursuant to the Securities Purchase Agreement (the "Cap
Allocation Amount"). In the event that any holder of Series H Preferred Stock
shall convert all of such holder's shares of Series H Preferred Stock into a
number of shares of Common Stock which, in the aggregate, is less than such
holder's Cap Allocation Amount, then the difference between such holder's Cap
Allocation Amount and the number of shares of Common Stock actually issued to
such holder shall be allocated to the respective Cap Allocation Amounts of the
remaining holders of Series H Preferred Stock on a pro rata basis in proportion
to the number of shares of Series H Preferred Stock then held by each such
holder. Nothing in this subparagraph 9(a) shall limit a holder's right to
convert its shares of Series H Preferred Stock.

          (b)  On each Conversion Date, the number of shares of Common Stock
underlying the Series H Preferred Stock to be issued to each holder (not
including the outstanding shares of Series H Preferred Stock or the unissued
shares of Common Stock underlying the Series H Preferred Stock) will not exceed
the number of such shares which, when aggregated with all other shares of Common
Stock then owned by such holder beneficially or deemed beneficially owned by
such holder, would result in any holder owning more than 4.99% of all of such
Common Stock as would be outstanding on such Conversion Date. The foregoing
limitation shall not apply in the event of an automatic conversion pursuant to
subparagraph 5(e).



                                      -8-
<PAGE>   9

     IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Designation to be signed by its President, and attested by its Secretary, this
24th day of November, 1998.


                                        StarBase Corporation


                                        By: /s/ William R. Stow, III
                                            ------------------------------------
                                            William R. Stow, III,
                                            Chief Executive Officer

Attest:

By: /s/ Douglas S. Norman
    -----------------------------------
    Douglas S. Norman,
    Assistant Secretary



                                      -9-
<PAGE>   10

                              STARBASE CORPORATION

                                CONVERSION NOTICE

Reference is made to the Certificate of Designation of StarBase Corporation (the
"CERTIFICATE OF DESIGNATION"). In accordance with and pursuant to the
Certificate of Designation, the undersigned hereby elects to convert the number
of shares of Series H Convertible Preferred Stock, par value $.01 per share (the
"PREFERRED SHARES"), of StarBase Corporation, a Delaware corporation (the
"COMPANY"), indicated below into shares of Common Stock, par value $.01 per
share (the "COMMON STOCK"), of the Company, by tendering the stock
certificate(s) representing the share(s) of Preferred Shares specified below as
of the date specified below.

     Date of Conversion: _______________________________________________________

     Number of Preferred Shares to be converted: _______________________________

     Stock certificate no(s). of Preferred Shares to be converted: _____________

     The Common Stock have been sold pursuant to the Registration Statement (as
     defined in the Registration Rights Agreement): YES ____ NO _____

Please confirm the following information:

     Conversion Price: _________________________________________________________

     Number of shares of Common Stock to be issued: ____________________________

Please issue the Common Stock into which the Preferred Shares are being
converted and, if applicable, any check drawn on an account of the Company in
the following name and to the following address:

     Issue to: _________________________________________________________________

               _________________________________________________________________

     Facsimile Number: _________________________________________________________

     Authorization: ____________________________________________________________

                    By:_________________________________________________________

                    Title:______________________________________________________



                                      -10-
<PAGE>   11

     Dated: ____________________________________________________________________

     Account Number:
      (if electronic book entry transfer):______________________________________

     Transaction Code Number
      (if electronic book entry transfer):______________________________________


                                 PRICES ATTACHED



                                      -11-