<PAGE>   1
                                                                   EXHIBIT 10.63


                           CONVERTIBLE PROMISSORY NOTE

$12,925,976.48                                            As of January 1, 1996


             FOR VALUE RECEIVED, the undersigned, CORNERSTONE PROPERTIES INC., a
Nevada corporation (together with its successors and assigns, hereafter referred
to as "CORNERSTONE" or "BORROWER"), promises to pay to the order of HINES
COLORADO LIMITED, a Colorado limited partnership (hereafter referred to as
"PAYEE"; Payee and/or any subsequent holder(s) hereof, hereafter referred to as
"HOLDER"), at Payee's address or at such other place as Holder shall designate
from time to time in writing, the principal sum of TWELVE MILLION NINE HUNDRED
TWENTY-FIVE THOUSAND NINE HUNDRED SEVENTY-SIX DOLLARS AND FORTY-EIGHT CENTS
($12,925,976.48) (which amount is hereinafter defined as the "PRINCIPAL SUM"),
together with interest thereon at the rates hereinafter set forth, on the
principal balance of this Note outstanding from time to time, together with all
other fees and charges hereinafter provided for, in same day funds and lawful
money of the United States of America that shall at the time of payment be legal
tender for the payment of all debts and dues, public and private.

             SECTION 1. CERTAIN DEFINITIONS. In addition to the terms defined
elsewhere in this Note, as used herein the following terms shall have the
indicated definitions unless otherwise specifically defined herein:

             "AFFILIATE" shall mean, with respect to any Person, any other
Person directly or indirectly controlling or controlled by, or under direct or
indirect common control with, such Person. For purposes of this definition, the
term "control" (including the correlative meanings of the terms "controlled by"
and "under common control with"), as used with respect to any Person, shall mean
the possession, directly or indirectly, of the power to direct or cause the
direction of the management policies of such Person, whether through the
ownership of voting securities or by contract or otherwise.

             "APPLICABLE RATE" shall mean, with respect to each applicable
Interest Period, an annual interest rate equal to the lesser of (a) eight and
eleven one-hundredths percent (8.11%) and (b) the LIBOR Determined Rate.

             "BASIS POINT" shall mean one one-hundredth (1/100th) of one
percentage point of interest.

             "BORROWER" shall include the maker(s) of this Note and all
person(s) or entity(ies) now or hereafter liable with respect to this Note,
whether as maker, principal, surety, guarantor, endorser or otherwise, each of
whom shall be jointly and severally liable for all of the obligations of the
maker(s) hereunder.

             "CLOSING PRICE" shall mean, on any day, the reported last sales
price on such day or, if such day is not a Trading Date, on the immediately
preceding Trading Date, or, in case no such sale takes place on the applicable
of such days, the average of the last reported closing bid and asked prices, in
each case on the Frankfurt Stock Exchange, or, if different, on the principal
securities exchange or Nasdaq National Market System on which Purchaser's

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Common Stock is then listed or admitted to trading, or, if not listed or
admitted to trading on any securities exchange or Nasdaq National Market System,
the average of the last closing bid and asked prices as furnished by any
broker/dealer selected in good faith from time to time by the Board of Directors
or the Administrative committee of the Board of Directors of Cornerstone for
that purpose.

             "CONVERSION DATE" shall have the meaning ascribed to such term in
Section 5(c) hereof.

             "CONVERSION PRICE" shall mean $14.30, as appropriately adjusted for
any stock split or other subdivision or consolidation of outstanding shares of
Purchaser's Common Stock, any declaration of a dividend or distribution payable
in shares of Purchaser's Common Stock, any capital reorganization or
reclassification or other transaction involving an increase, reduction or change
in the number of outstanding shares of Purchaser's Common Stock, or any
consolidation or merger of Borrower with another corporation or entity or the
adoption by Borrower of a plan of exchange affecting Purchaser's Common Stock or
any distribution to holder of Purchaser's Common Stock of securities or property
(other than (a) normal cash dividends and distributions and (b) stock dividends
or distributions previously referred to in this definition).

             "INTEREST PERIOD" shall mean a period of time commencing on the
date following the expiration of each immediately preceding Interest Period and
ending on the date thirty (30) days following such commencement date; provided
that (a) in the case of the first Interest Period, such period shall commence on
the date hereof; and (b) if any Interest Period shall end on a day other than a
LIBOR Day, such Interest Period shall be extended to the next succeeding day
which is a LIBOR Day unless such succeeding day would fall in the next calendar
month, in which event such Interest Period shall end on the immediately
preceding LIBOR Day.

             "LBC" shall mean Lincoln Building Corporation.

             "LIBO RATE" shall mean the rate of interest per annum (expressed as
an annual rate rounded to the nearest one-hundredth of a Basis Point) equal to
the London interbank offered rate for deposits in U.S. dollars for a period
equal to the applicable Interest Period as of 1:00 p.m. local London time, three
LIBOR Days before the first day of such Interest Period. The applicable LIBO
Rate shall be determined by reference to the Telerate, Inc. display designated
as page 3750 -- "British Bankers Association Interest Settlement Rates" (or such
other page as may replace such page on the Telerate, Inc. service for the
purpose of displaying London interbank offered rates); provided, however, that
if Telerate, Inc. shall not publish or shall cease publication of such
information, the applicable LIBO Rate shall be determined by reference to the
highest rate shown on the display designated as page "LIBO" on the Reuters
Monitor Money Rates Service (or such other page as may replace the LIBO page on
that service for the purpose of displaying London interbank offered rates of
major banks); and provided further that if Reuters Monitor Money Rates Service
shall not publish or shall cease publication of such information, the applicable
LIBO Rate shall be determined by reference to the rate at which deposits in U.S.
dollars are offered by the principal office of Deutsche Bank AG in the London
interbank market for the applicable Interest Period.
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             "LIBOR DAY" shall mean any day of the year on which dealings are
carried on in the London interbank market and commercial banks are open for
business in London, England.

             "LIBOR DETERMINED RATE" shall mean, with respect to any applicable
Interest Period, a rate per annum equal to the LIBO Rate plus fifty (50) Basis
Points.

             "MATURITY DATE" shall mean the fifth (5th) anniversary of the date
hereof.

             "MATURITY DATE EFFECTIVE PRICE" shall mean the lesser of (i) the
average of the Closing Price per share of Purchaser's Common Stock for the last
five (5) consecutive Trading Dates immediately preceding the date on which
Borrower delivers to Holder the notice described in Section 5(b) hereof, and, if
the Closing Prices are not quoted in U.S. dollars, with each such Closing Price
being converted to U.S. dollars using the average quoted currency to U.S. dollar
exchange rate published in The Wall Street Journal over the same such five (5)
consecutive Trading Dates and (ii) the Conversion Price.

             "PERSON" shall mean any individual, partnership, corporation,
limited liability company, trust, unincorporated association or joint venture, a
government or any department or agency thereof, or any other entity.

             "PRIME RATE" shall mean the rate of interest announced publicly in
New York, New York, from time to time, by Citibank, N.A., or its successor from
time to time, as its base lending rate.

             "PURCHASE AGREEMENT" shall mean that certain Agreement for Purchase
and Sale of Partnership Interests in 1700 Lincoln Limited dated as of January
__, 1996 between Hines Colorado Limited, as Seller, and Cornerstone, as
Purchaser.

             "PURCHASER'S COMMON STOCK" shall have the meaning ascribed to such
term in the Purchase Agreement.

             "RENT NOTE" shall mean that certain Amended and Restated Promissory
Note, dated December 30, 1988, in the original principal amount of $10,000,000
made by Holder in favor of LBC, which note was subsequently (i) assigned by LBC
to Borrower pursuant to that certain Assignment of Note and Liens, dated
December 30, 1988, and (ii) modified pursuant to that certain Second Amended and
Restated Promissory Note, dated as of the date hereof, made by Holder in favor
of Borrower.

             "SHARE LIMIT" shall mean the maximum (i) number of shares of
Purchaser's Common Stock or (ii) if greater, value of outstanding shares of
Purchaser's Common Stock, each as permitted to be held by Holder pursuant to the
Articles of Incorporation of Borrower, as in effect as of the date hereof;
provided, however, that if from time to time, in order to preserve Borrower's
status as a real estate investment trust under the Internal Revenue Code of
1986, as amended, the Board of Directors of Borrower shall adopt a resolution or
the shareholders of Borrower shall amend the Articles of Incorporation, which
resolution or amendment reduces the aforesaid maximum number or value of
outstanding shares permitted to be held by Holder, then, as used in this Note,
Share Limit shall mean the maximum (x)
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number of shares of Purchaser's Common Stock or (y) if greater, value of
outstanding shares of Purchaser's Common Stock, each as permitted to be held by
Holder pursuant to such resolution or amendment, as applicable, as in effect on
the Conversion Date or the Maturity Date, as applicable.

             "STOCK PLEDGE" shall mean a pledge by Holder to Borrower of the
number of shares of Purchaser's Common Stock having a market value of no less
than 125% of the amount of principal and interest owing under the Rent Note on
the Conversion Date, in form and substance reasonably satisfactory to Borrower.

             "TRADING DATE" shall mean a date on which the Frankfurt Stock
Exchange or other applicable securities exchange or market used for determining
the Closing Price is open for the transaction of business.

             SECTION 2. INTEREST RATE. Subject to the terms and conditions
hereof, this Note shall bear interest on the Principal Sum at a floating rate of
interest from time to time equal to the Applicable Rate.

             SECTION 3. PAYMENT OF PRINCIPAL AND INTEREST. (a) From the date
hereof up to and including the Maturity Date, interest on the Principal Sum at
the Applicable Rate shall be due and payable in consecutive monthly
installments, due on the first day of each and every calendar month, in arrears,
commencing on the first day of the first calendar month following the date of
this Note, and continuing on the first day of each month through the Maturity
Date. Each such installment of interest shall be accompanied by a written
statement prepared by Borrower setting forth in reasonable detail the
calculation of such installment, including Borrower's determination of the
Applicable Rate for the relevant Interest Period.

             (b) Borrower shall pay in full to Holder the Principal Sum and all
accrued but unpaid interest thereon on the Maturity Date.

             SECTION 4. COMPUTATIONS. All computations of interest on a day to
day basis shall be made by Holder on the basis of a year of 360 days and a month
of 30 days for the actual number of days elapsed in the period for which such
interest is payable.

             SECTION 5. PAYMENTS. (a) All payments made under this Note shall be
applied, first, to fees and expenses due and payable by Borrower pursuant to
this Note, second, in reduction of accrued and unpaid interest, and, third, any
remaining amount in reduction of the Principal Sum. This Note may not be prepaid
except in accordance with the provisions of Section 5(c) hereof.

             (b) Notwithstanding anything in the first paragraph of this Note to
the contrary and subject to Sections 5(e) and 5(f) hereof, Borrower may elect
(provided that Borrower has given Holder notice of such election in writing on a
date which is not earlier than ninety (90) days' prior to the Maturity Date and
not later than thirty (30) days' prior to said Maturity Date) to pay the
Principal Sum on, but not prior to, the Maturity Date by issuing and delivering
to Holder duly authorized, validly issued, fully paid and non-assessable shares
of Purchaser's Common Stock. In the event Borrower makes such election, the
number of shares of Purchaser's Common Stock issuable by Borrower to Holder on
the Maturity Date
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shall equal (i) the Principal Sum divided by (ii) the Maturity Date Effective
Price, rounded down to the nearest whole share with Holder receiving cash for
any fractional share resulting from such calculation. Borrower may not make the
election provided in this Section 5(b) if this Note is converted pursuant to
Section 5(c) below.

             (c) At the option of Holder, this Note will be convertible, in
whole but not in part, at any time after the first anniversary of the date
hereof, into shares of Purchaser's Common Stock. In order to convert this Note
pursuant to this Section 5(c), Holder shall give Borrower no fewer than thirty
(30) days' prior written notice of the date upon which such conversion shall
occur ("CONVERSION DATE"). Subject to Section 5(f) hereof, the number of shares
of Purchaser's Common Stock issuable on the Conversion Date shall equal (i) the
Principal Sum, divided by (ii) the Conversion Price, rounded down to the nearest
whole share with Holder receiving cash for any fractional share resulting from
such calculation. In the event that any amounts remain outstanding under the
Rent Note as of the Conversion Date, Holder shall execute and deliver to
Borrower the Stock Pledge and shall deliver possession of the appropriate number
of shares to Borrower in accordance with the Stock Pledge. Holder may not
exercise its right to convert this Note pursuant to this Section 5(c) if
Borrower elects to pay the principal sum in shares of Purchaser's Common Stock
pursuant to Section 5(b) above.

             (d) On the Maturity Date (if Borrower delivers to Holder the notice
described in Section 5(b) hereof) or the Conversion Date, as applicable,
Borrower shall issue and deliver or cause to be issued and delivered to Holder,
issued in the name of Holder or, if Holder shall request in writing, an
Affiliate of Holder, one or more certificates for the number of full shares of
Purchaser's Common Stock issuable on the Maturity Date or the Conversion Date
pursuant to Section 5(b) or 5(c), as applicable. Such issuance of shares and the
conversion of this Note shall be deemed effected as of the close of business on
the Maturity Date or the Conversion Date, as applicable, and the Person in whose
name any certificates for shares of Purchaser's Common Stock shall be issuable
upon such issuance and conversion shall be deemed to have become the holder of
record of the shares of Purchaser's Common Stock represented thereby on such
date.

             (e) Borrower may elect to pay the Principal Sum by issuing and
delivering shares of Purchaser's Common Stock to Holder pursuant to Section 5(b)
only if the following conditions have been satisfied (and an officer of Borrower
certifies as to the satisfaction of such conditions) or waived in writing by
Holder; (i) the shares to be so issued to Holder in payment of Borrower's
obligations hereunder have been listed, and are tradeable, on the Frankfurt
Stock Exchange or on a national stock exchange or the Nasdaq National Market
System in the United States; and (ii) the representations and warranties in
Sections 3.02(a), 3.02(b), 3.02(c), 3.02(f) and 3.02(g) of the Purchase
Agreement are true and correct as of the date of such election and the date of
issuance of such shares.

             (f) Notwithstanding anything herein to the contrary but subject to
Section 14 hereof, if the issuance of shares of Purchaser's Common Stock
pursuant to Section 5(b) or 5(c), as applicable, would result in Holder becoming
the owner of a number of shares of Purchaser's Common Stock exceeding the Share
Limit, then on the Maturity Date (if Borrower delivers to Holder the notice
described in Section 5(b) hereof) or the Conversion Date, as applicable,
Borrower shall:
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                  (A) issue and deliver to Holder a number of duly authorized,
         validly issued, fully paid and nonassessable shares of Purchaser's
         Common Stock equal to (1) the number of shares otherwise required to be
         issued and delivered pursuant to Section 5(b) or 5(c), as applicable,
         minus (2) the number of shares that would, if so issued, exceed the
         Share Limit (such shares referred to in this clause (2), the "EXCESS
         SHARES");

                  (B) in the event of an issuance of shares pursuant to Section
         5(b) hereof, pay to Holder an amount in lawful money of the United
         States of America equal to the product of (1) the Excess Shares,
         multiplied by (2) the average of the Closing Price per share of
         Purchaser's Common Stock for the last five (5) consecutive Trading
         Dates immediately preceding the date on which Borrower delivers to
         Holder the notice described in Section 5(b) hereof, and, if the Closing
         Prices are not quoted in U.S. dollars, with each such Closing Price
         being converted to U.S. dollars using the average quoted currency to
         U.S. dollars exchange rate published in The Wall Street Journal over
         the same such five (5) consecutive Trading Dates.

                  (C) in the event of an issuance of shares pursuant to Section
         5(c) hereof, pay to Holder an amount in lawful money of the United
         Stated of America equal to the product of (1) the Excess Shares,
         multiplied by (2) the average of the Closing Price per share of
         Purchaser's Common Stock for the last five (5) consecutive Trading
         Dates immediately preceding the date on which Holder delivers to
         Borrower the notice described in Section 5(c) hereof, and, if the
         Closing Prices are not quoted in U.S. dollars, with each such Closing
         Price being converted to U.S. dollars using the average quoted currency
         to U.S. dollars exchange rate published in The Wall Street Journal over
         the same such five (5) consecutive Trading Dates.

             SECTION 6. INTEREST UPON DEFAULT. In the event that any payment of
principal, interest or late charges under this Note is not paid when due, such
failure shall constitute a default hereunder and the entire unpaid Principal Sum
under this Note shall bear interest from the due date thereof for so long as
such default remains uncured at the per annum rate which is two hundred (200)
Basis Points above the Prime Rate.

             SECTION 7. RESERVATION OF SHARES OF PURCHASER'S COMMON STOCK.
Borrower shall at all times keep reserved, free from preemptive rights, out of
its authorized Purchaser's Common Stock, a number of shares of Purchaser's
Common Stock sufficient to provide for the conversion of this Note. Borrower
covenants that all shares of Purchaser's Common Stock issuable upon conversion
of this Note, upon issuance in accordance with this Note, will be duly
authorized, validly issued, fully paid, nonassessable and free of preemptive
rights, stock transfer and other similar taxes payable by Borrower and liens
(except any liens created by Holder), and will not be subject to any
restrictions on voting or transfer except for any restrictions on voting or
transfer provided in Borrower's Articles of Incorporation or as otherwise
provided by law. If issuance or delivery of any of the shares of Purchaser's
Common Stock upon conversion of this Note requires registration with or consent
of any securities exchange or market or any governmental authority, then, unless
caused by reason of the failure of any of Holder's representations and
warranties in the Purchase Agreement to be true and correct as of the Conversion
Date or Maturity Date, as applicable, Borrower shall, in good faith and as
expeditiously as possible, endeavor to secure such registration or consent, as
the case may be; provided, however, that nothing in this Section 7 shall be
deemed to affect in
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any way the obligations of Borrower to issue shares of Purchaser's Common Stock
upon conversion of this Note as provided in Section 5. Without limiting the
generality of the foregoing, Borrower shall take such action as may be necessary
or appropriate to list the shares of Purchaser's Common Stock issuable pursuant
to this Note with the Frankfurt Stock Exchange, or, if different, on the
principal securities exchange or Nasdaq National Market System on which
Purchaser's Common Stock is listed or admitted to trading on the date of
issuance.

             SECTION 8. MERGERS, CONSOLIDATIONS AND SALES OF ASSETS. If, at any
time before the payment in full and discharge of this Note, Borrower shall (i)
consolidate with or merge into any other Person and shall not be the continuing
or surviving corporation in such consolidation or merger, (ii) permit any other
Person to consolidate or merge into Borrower and Borrower shall be the
continuing or surviving corporation but, in connection with such consolidation
or merger, Purchaser's Common Stock shall be changed into or converted into
stock, other securities or assets of any other Person, (iii) transfer all or
substantially all of its assets to any other Person or (iv) effect a capital
reorganization or reclassification of Purchaser's Common Stock, Borrower or such
successor, as the case may be, shall covenant in the constituent documents
effecting any of the foregoing transactions that Holder thereafter shall have
the right to obtain upon the exercise of its conversion rights pursuant to this
Note, in lieu of each share of Purchaser's Common Stock theretofore issuable
upon exercise of such conversion rights, the kind and amount of stock, other
securities or assets that it would have owned immediately after such
consolidation, merger, transfer, reorganization or reclassification if it had
converted this Note immediately before the effective date of such transaction.
The provisions of this Section 8 shall similarly apply to successive
consolidations, mergers, transfers or reclassifications.

             SECTION 9. ATTORNEYS' FEES. If this Note is placed in the hands of
an attorney for collection or is collected through any legal or administrative
proceeding, including, without limitation, bankruptcy or insolvency proceedings,
following a default hereunder by Borrower, Borrower promises to pay, to the
extent permitted by law, reasonable attorneys' fees, including fees incurred for
trial and appellate proceedings.

             SECTION 10. WAIVER. Borrower hereby waives presentment for payment,
demand, protest, notice of nonpayment, demand, default, dishonor and protest.

             SECTION 11. FORBEARANCE. Holder shall not be deemed to have waived
any of Holder's rights or remedies under this Note unless such waiver is express
and in a writing signed by Holder, and no delay or omission by Holder in
exercising, or failure by Holder on any one or more occasions to exercise, any
of Holder's rights hereunder or at law or in equity, shall be construed as a
novation of this Note or shall operate as a waiver or prevent the subsequent
exercise of any or all of such rights. Acceptance by Holder of any portion or
all of any sum payable hereunder whether before, on or after the due date of
such payment, shall not be a waiver of Holder's right either to require prompt
payment when due of all other sums payable hereunder. A waiver of any right on
one occasion shall not be construed as a waiver of Holder's right to insist
thereafter upon strict compliance with the terms hereof without previous notice
of such intention being given to Borrower, and no exercise of any right by
Holder shall constitute or be deemed to constitute an election of remedies by
Holder precluding the subsequent exercise by Holder of any or all of the rights,
powers and remedies available to it hereunder or at law or in equity. Borrower
expressly waives the benefit of any
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                                       8


statute or rule of law or equity now provided, or which may hereafter be
provided, which would produce a result contrary to, or in conflict with, the
foregoing. Borrower consents to any and all renewals and extensions in the time
of payment hereof without in any way affecting the liability of Borrower or any
person liable or to become liable with respect to any indebtedness evidenced
hereby. No expansion of the time for the payment of this Note or any installment
due hereunder, made by agreement with any person now or hereafter liable for the
payment of this Note shall operate to release, discharge, modify, change or
affect the original liability of Borrower under this Note, either in whole or in
part, unless Holder agrees otherwise in writing.

             SECTION 12. APPLICABLE LAW. This Note shall be governed by,
enforced under and interpreted in accordance with the substantive laws of the
State of New York without regard to the choice of law doctrine of such state.

             SECTION 13. JURISDICTION. At the option of Holder, an action may be
brought to enforce this Note in the appropriate court in the County and State of
New York, or in the United States District Court for the Southern District of
New York. Borrower and all signers or endorsers hereof consent to venue and
jurisdiction in such courts and Borrower hereby consents to service of process
in accordance with the applicable New York law.

             SECTION 14. LIMIT ON INTEREST. If, from any circumstances
whatsoever, fulfillment of any provision of this Note, at the time performance
of such provision shall be due, shall involve transcending the limit on interest
presently prescribed by any applicable usury statute or any other applicable
law, with regard to obligations of like character and amount, then Holder may at
its option (a) declare the entire indebtedness evidenced hereby, including
interest, if any, and all other sums owing, immediately due and payable, (b)
reduce the obligations to be fulfilled to such limit on interest or (c) apply
the amount that would exceed such limit on interest to the reduction of the
outstanding principal balance of this Note, and not to the payment of interest,
with the same force and effect as though Borrower had specifically designated
such sums to be so applied to principal and Holder had agreed to accept such
extra payment(s) as a prepayment, so that in no event shall any exaction be
possible under this Note that is in excess of the applicable limit on interest.
It is the intention of Borrower and Holder not to create any obligation in
excess of the amount allowable by applicable law. The provisions of this
paragraph shall control every other provision of this Note.

             SECTION 15. TIME OF ESSENCE. TIME IS OF THE ESSENCE in complying
with all of the terms, provisions and conditions of this Note.

             SECTION 16. REMEDIES UPON DEFAULT. All obligations of Borrower to
Holder, direct or indirect, absolute or contingent, now existing or hereafter
arising under this Note, shall, at the option of Holder, become immediately due
and payable without further notice or demand, and Holder shall have and may
exercise any or all of the rights and remedies provided herein in the event of
any default in any (a) payment of the Principal Sum of this Note; (b) payment of
interest on this Note, which default remains uncured for a period of five (5)
days after receipt by Borrower of notice from Holder of such default; or (c)
performance of any non-monetary obligation contained in this Note, which default
is uncured for a period of thirty (30) days after receipt by Borrower of notice
from Holder that such performance is due.
<PAGE>   9
                                       9


             SECTION 17. ILLEGALITY. If any position in this Note shall be held
invalid, illegal or unenforceable in any jurisdiction, the validity, legality or
enforceability of any defective provision shall not affect the validity,
legality or enforceability of any other provision hereof, which shall remain in
full force and effect.

             SECTION 18. NOTICES. All notices to Borrower or Holder given
hereunder shall be in writing and may be given or served by depositing the same
in the United States mail, postage prepaid, registered or certified and
addressed to the party to be notified, with return receipt requested; by
overnight courier to such party; or by delivering the same in person to such
party. If mailed as described above, notice shall be deemed received three days
after deposit in the United States mail. Notice given in any other manner shall
be effective only if and when actually received by the party to be notified. For
purposes of notice, the addresses of the parties shall, until changed as
hereinafter provided, be as follows:

                           If to Borrower:

                                    Cornerstone Properties Inc.
                                    31 West 52nd Street
                                    Suite 1600
                                    New York, New York  10019
                                    Attention:  President

                           with a copy to:

                                    Shearman & Sterling
                                    153 East 53rd Street
                                    New York, New York  10022
                                    Attention: Real Estate Notices
                                               02189-00006/Timothy G. Little

                           If to Holder:

                                    Hines Colorado Limited
                                    Hines Interests Limited Partnership
                                    Three First National Plaza
                                    Suite 440
                                    Chicago, Illinois  60602
                                    Attention:  Mr. David McGinnis

                           with a copy to:

                                    Baker & Botts, L.L.P.
                                    2001 Ross Avenue
                                    Dallas, Texas  75201
                                    Attention: James A. Taylor, Esq.

Either party may change its address for notices herein to any address within the
United States by notice delivered as provided above at least 15 days prior to
the effective date of such change. Each party may designate up to two additional
parties in the United States to whom
<PAGE>   10
                                       10


copies of notices shall be delivered hereunder, by notice delivered as provided
above.

             SECTION 19. AMENDMENT. This Note may not be waived, changed,
modified or discharged orally, except by an agreement in writing signed by the
party against whom the enforcement of waiver, change, modification or discharge
is sought.

             SECTION 20. SEPARATE ACTIONS. Principal and interest owing on this
Note may be recovered in a separate action, or may be recovered in a single
action. Holder, or any person claiming by, through, or under Holder, shall have
the absolute right to seek one or more money judgments in each such cause of
action based on this Note.

             SECTION 21. PARTIES BOUND. The singular shall include the plural
and vice versa. The obligations and liabilities hereunder are joint and several
and shall be binding upon the heirs, successors, legal representatives,
endorsers and assigns of the parties hereof.

             SECTION 22. HEADINGS. The underlined words appearing at the
commencement of the paragraphs are included only as a guide to the contents
thereof and are not to be considered as controlling, enlarging or restructuring
the language or meaning of those paragraphs.

             SECTION 23. SET-OFF. In the event that Holder shall default in its
obligations to make any payment of interest or principal due from time to time
under the Rent Note, then, in addition to and without limitation or impairment
of any rights, remedies or security that Borrower may otherwise have with
respect to the Rent Note, Borrower shall be entitled to offset against its
obligations under this Note all amounts then due and payable by Holder as maker
under the Rent Note.

             SECTION 24. NO WAIVER; REMEDIES CUMULATIVE. No failure on the part
of Holder to exercise, and no delay in exercising, any right hereunder shall
operate as a waiver thereof; nor shall any single or partial exercise of any
right hereunder preclude any other or further exercise thereof or the exercise
of any other right. The remedies herein provided are cumulative and not
exclusive of any remedies provided by law. In particular, in the event Borrower
fails to deliver to Holder the shares of Purchaser's Common Stock that may be
required to be so delivered pursuant to Sections 5(b) or 5(c) hereof, Holder
shall be entitled to any and all remedies available hereunder, in law and/or in
equity with respect to such failure and shall not be limited to collection of
the Principal Sum and accrued interest thereon.

                                      * * *

                            [SIGNATURES ON NEXT PAGE]
<PAGE>   11
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             SIGNED AND DELIVERED by Borrower on the date first hereinabove
written.


                                        CORNERSTONE PROPERTIES INC.



                                        By:_____________________________
                                             Scott M. Dalrymple
                                             Vice President




                                        By:_____________________________
                                             Kevin P. Mahoney
                                             Vice President