Document:

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                                                                   EXHIBIT 10.12

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 AS
AMENDED, OR ANY STATE SECURITIES LAWS. THEY MAY NOT BE SOLD, OFFERED FOR SALE,
PLEDGED, OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT
RELATED THERETO OR AN OPINION OF COUNSEL (WHICH MAY BE COMPANY COUNSEL)
REASONABLY SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES
LAWS.

                               WARRANT AGREEMENT

             To Purchase Shares of the Series C Preferred Stock of

                             ALIGN TECHNOLOGY INC.

              Dated as of January 7, 2000 (the "Effective Date")

          WHEREAS, Align Technology Incorporated, a Delaware corporation (the
"Company") has entered into a Loan and Security Agreement dated as of January 7,
2000, and related Promissory Note(s) (collectively, the "Loans") with Comdisco,
Inc., a Delaware corporation (the "Warrantholder'); and

          WHEREAS, the Company desires to grant to Warrantholder, in
consideration for such Loans, the right to purchase shares of its Series C
Preferred Stock;

          NOW, THEREFORE, in consideration of the Warrantholder executing and
delivering such Loans and in consideration of mutual covenants and agreements
contained herein, the Company and Warrantholder agree as follows:

1.        GRANT OF THE RIGHT TO PURCHASE PREFERRED STOCK.
          ----------------------------------------------

          The Company hereby grants to the Warrantholder, and the Warrantholder
is entitled, upon the terms and subject to the conditions hereinafter set forth,
to subscribe to and purchase, from the Company, 56,250 fully paid and non-
assessable shares of the Company's Series C Preferred Stock ("Preferred Stock")
at a purchase price of $8.00 per share (the "Exercise Price").  The number and
purchase price of such shares are subject to adjustment as provided in Section 8
hereof.

2.        TERM OF THE WARRANT AGREEMENT.
          -----------------------------

          Except as otherwise provided for herein, the term of this Warrant
Agreement and the right to purchase Preferred Stock as granted herein shall
commence on the Effective Date and shall be exercisable for a period of (i) ten
(10) years or (ii) five (5) years from the effective date of the Company's
initial public offering, whichever is shorter.

          Notwithstanding the term of this Warrant Agreement fixed pursuant to
the above paragraph, the right to purchase Preferred Stock as granted herein
shall expire, if not previously

                                       1.
<PAGE>

exercised immediately upon the closing of a merger or consolidation of the
Company with or into another corporation or entity when the Company's
stockholders immediately before the consummation of such transaction do not hold
at least 50% of the outstanding securities of the surviving entity, or the sale
of all or substantially all of the Company's properties and assets to any other
person (collectively, a "Merger"); provided in which Warrantholder realizes a
value for its shares equal to or greater than $9.00 per share.

          The Company shall notify the Warrantholder if the Merger is proposed
in accordance with the terms of 8(f) hereof, and if the Company fails to deliver
such written notice, then notwithstanding anything to the contrary in this
Warrant Agreement, the rights to purchase the Company's Preferred Stock shall
not expire until the Company has delivered written notice of the Merger and the
notice period set forth in 8(f) hereof has expired.  Such notice shall also
contain such details of the proposed Merger as are reasonable in the
circumstances.  If such closing does not take place, the Company shall promptly
notify the Warrantholder that such proposed transaction has been terminated, and
the Warrantholder may rescind any exercise of its purchase rights promptly after
such notice of termination of the proposed transaction if the exercise of
Warrants has occurred after the Company notified the Warrantholder that the
Merger was proposed.  In the event of such recission, the Warrants will continue
to be exercisable on the same terms and conditions contained herein.

3.        EXERCISE OF THE PURCHASE RIGHTS.
          --------------------------------

          The purchase rights set forth in this Warrant Agreement are
exercisable by the Warrantholder, in whole or in part, at any time, or from time
to time, prior to the expiration of the term set forth in Section 2 above, by
tendering to the Company at its principal office a notice of exercise in the
form attached hereto as Exhibit I (the "Notice of Exercise"), duly completed and
executed.  Promptly upon receipt of the Notice of Exercise and the payment of
the purchase price in accordance with the terms set forth below, and in no event
later than twenty-one (21) days thereafter, the Company shall issue to the
Warrantholder a certificate for the number of shares of Preferred Stock
purchased and shall execute the acknowledgment of exercise in the form attached
hereto as Exhibit 11 (the "Acknowledgment of Exercise") indicating the number of
shares which remain subject to future purchases, if any.

          The Exercise Price may be paid at the Warrantholder's election either
(i) by cash or check, or (ii) by surrender of Warrants ("Net Issuance") as
determined below.  If the Warrantholder elects the Net Issuance method, the
Company will issue Preferred Stock in accordance with the following formula:

                    X = Y(A-B)
                        ------
                          A

          Where:  X =  the number of shares of Preferred Stock to be issued to
                       the Warrantholder.

                  Y =  the number of shares of Preferred Stock requested to be
                       exercised under this Warrant Agreement.

                  A =  the fair market value of one (1) share of Preferred
                       Stock.

                                       2.
<PAGE>

                  B =  the Exercise Price.

          For purposes of the above calculation, current fair market value of
Preferred Stock shall mean with respect to each share of Preferred Stock:

                       (i)    if the exercise is in connection with an initial
                  public offering of the Company's Common Stock, and if the
                  Company's Registration Statement relating to such public
                  offering has been declared effective by the SEC, then the fair
                  market value per share shall be the product of (x) the initial
                  "Price to Public" specified in the final prospectus with
                  respect to the offering and (y) the number of shares of Common
                  Stock into which each share of Preferred Stock- is convertible
                  at the time of such exercise;

                       (ii)   if this Warrant is exercised after, and not in
                  connection with the Company's initial public offering, and:

                              (a) if traded on a securities exchange, the fair
                       market value shall be deemed to be the product of (x) the
                       average of the closing prices over a five (5) day period
                       ending three days before the day the current fair market
                       value of the securities is being determined and (y) the
                       number of shares of Common Stock into which each share of
                       Preferred Stock is convertible at the time of such
                       exercise; or

                              (b) if actively traded over-the-counter, the fair
                       market value shall be deemed to be the product of (x) the
                       average of the closing bid and asked prices quoted on the
                       NASDAQ system (or similar system) over the five (5) day
                       period ending three days before the day the current fair
                       market value of the securities is being determined and
                       (y) the number of shares of Common Stock into which each
                       share of Preferred Stock is convertible at the time of
                       such exercise;

                       (iii)  if at any time the Common Stock is not listed on
                  any securities exchange or quoted in the NASDAQ System or the
                  over-the-counter market, the current fair market value of
                  Preferred Stock shall be the product of (x) the highest price
                  per share which the Company could obtain from a willing buyer
                  (not a current employee or director) for shares of Common
                  Stock sold by the Company, from authorized but unissued
                  shares, as determined in good faith by its Board of Directors
                  and (y) the number of shares of Common Stock into which each
                  share of Preferred Stock is convertible at the time of such
                  exercise, unless the Company shall become subject to a merger,
                  acquisition or other consolidation pursuant to which the
                  Company is not the surviving party, in which case the fair
                  market value of Preferred Stock shall be deemed to be the
                  value received by the holders of the Company's Preferred Stock
                  on a common equivalent basis pursuant to such merger or
                  acquisition.

          Upon partial exercise by either cash or Net Issuance, the Company
shall promptly issue an amended Warrant Agreement representing the remaining
number of shares purchasable

                                       3.
<PAGE>

hereunder. All other terms and conditions of such amended Warrant Agreement
shall be identical to those contained herein, including, but not limited to the
Effective Date hereof.

4.   RESERVATION OF SHARES.
     ----------------------

     (a)  Authorization and Reservation of Shares. During the term of this
          ----------------------------------------
Warrant Agreement, the Company will at all times have authorized and reserved a
sufficient number of shares of its Preferred Stock to provide for the exercise
of the rights to purchase Preferred Stock as provided for herein.

     (b)  Registration or Listing. If any shares of Preferred Stock required to
          ------------------------
be reserved hereunder require registration with or approval of any governmental
authority under any Federal or State law (other than any registration under the
Securities Act of 1933, as amended ("1933 Act"), as then in effect, or any
similar Federal statute then enforced, or any state securities law, required by
reason of any transfer involved in such conversion), or listing on any domestic
securities exchange, before such shares may be issued upon conversion, the
Company will, at its expense and as expeditiously as possible, use its best
efforts to cause such shares to be duly registered, listed or approved for
listing on such domestic securities exchange, as the case may be.

5.   NO FRACTIONAL SHARES OR SCRIP.
     ------------------------------

     No fractional shares or scrip representing fractional shares shall be
issued upon the exercise of the Warrant, but in lieu of such fractional shares
the Company shall make a cash payment therefor upon the basis of the Exercise
Price then in effect.

6.   NO RIGHTS AS SHAREHOLDER.
     -------------------------

     This Warrant Agreement does not entitle the Warrantholder to any voting
rights or other rights as a shareholder of the Company prior to the exercise of
the Warrant.

7.   WARRANTHOLDER REGISTRY.
     -----------------------

     The Company shall maintain a registry showing the name and address of the
registered holder of this Warrant Agreement.

8.   ADJUSTMENT RIGHTS.
     ------------------

     The purchase price per share and the number of shares of Preferred Stock
purchasable hereunder are subject to adjustment, as follows:

     (a)  Capital Reorganization.  If at any time there shall be a capital
          ----------------------
reorganization of the shares of the Company's stock (other than a combination,
reclassification, exchange or subdivision of shares otherwise provided for
herein), or a merger or consolidation of the Company with or into another
corporation whether or not the Company is the surviving corporation, where the
Company's Stockholders before such transaction do not hold at least 50% of the
outstanding securities of the successor entity after such transaction
(hereinafter referred to as a "Reorganization"), then, as a part of such
Reorganization, lawful provision shall be made so

                                       4.
<PAGE>

that the Warrantholder shall thereafter be entitled to receive, upon exercise of
the Warrant, the number of shares of preferred stock or other securities of the
successor company resulting from such Reorganization, equivalent in value to
that which would have been issuable if Warrantholder had exercised this Warrant
immediately prior to the Reorganization. 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 Agreement
with respect to the rights and interest of the Warrantholder after the
Reorganization to the end that the provisions of this Warrant Agreement
(including adjustments of the Exercise Price and number of shares of Preferred
Stock purchasable) shall be applicable to the greatest extent possible.

     (b)  Reclassification of Shares.  If the Company at any time shall, by
          --------------------------
combination, reclassification, exchange or subdivision of securities or
otherwise, change any of the securities as to which purchase rights under this
Warrant Agreement exist into the same or a different number of securities of any
other class or classes, this Warrant Agreement shall thereafter represent the
right to acquire such number and kind of securities as would have been issuable
as the result of such change with respect to the securities which were subject
to the purchase rights under this Warrant Agreement immediately prior to such
combination, reclassification, exchange, subdivision or other change.

     (c)  Subdivision or Combination of Shares.  If the Company at any time
          ------------------------------------
shall combine or subdivide its Preferred Stock, the Exercise Price shall be
proportionately decreased in the case of a subdivision, or proportionately
increased in the case of a combination.

     (d)  Stock Dividends.  If the Company at any time shall pay a dividend
          ---------------
payable in, or make any other distribution (except any distribution specifically
provided for in the foregoing subsections (a) or (b)) of the Company's Preferred
Stock, then the Exercise Price shall be adjusted, from and after the record date
of such dividend or distribution, to that price determined by multiplying the
Exercise Price in effect immediately prior to such record date by a fraction (i)
the numerator of which shall be the total number of all shares of the Company's
Preferred Stock outstanding immediately prior to such dividend or distribution,
and (ii) the denominator of which shall be the total number of all shares of the
Company's Preferred Stock outstanding immediately after such dividend or
distribution.  The Warrantholder shall thereafter be entitled to purchase, at
the Exercise Price resulting from such adjustment, the number of shares of
Preferred Stock (calculated to the nearest whole share) obtained by multiplying
the Exercise Price in effect immediately prior to such adjustment by the number
of shares of Preferred Stock issuable upon the exercise hereof immediately prior
to such adjustment and dividing the product thereof by the Exercise Price
resulting from such adjustment.

     (e)  Antidilution Rights.  Additional antidilution rights applicable to
          -------------------
the Preferred Stock purchasable hereunder are as set forth in the Company's
Certificate of Incorporation, as amended through the Effective Date, a true and
complete copy of which is attached hereto as Exhibit IV (the "Charter").  The
Company shall promptly provide the Warrantholder with any restatement,
amendment, modification or waiver of the Charter.  The Company shall provide
Warrantholder with prior written notice of any issuance of its stock or other
equity security to occur after the Effective Date of this Warrant, which notice
shall include (a) the price at which

                                       5.
<PAGE>

such stock or security is to be sold, (b) the number of shares to be issued, and
(c) such other information as necessary for Warrantholder to determine if a
dilutive event has occurred.

     (f)  Notice of Adjustments.  If:  (i) the Company shall declare any
          ---------------------
dividend or distribution upon its stock, whether in cash, property, stock or
other securities; (ii) the Company shall offer for subscription pro rata to the
holders of any class of its Preferred or other convertible stock any additional
shares of stock of any class or other rights; (iii) there shall be any Merger;
(Iv) there shall be any Reorganization; (v) there shall be an initial public
offering; or (vi) there shall be any voluntary dissolution, liquidation or
winding up of the Company; then, in connection with each such event, the Company
shall send to the Warrantholder: (A) at least twenty (20) days'- prior written
notice of the date on which the books of the Company shall close or a record
shall be taken for such dividend, distribution, subscription rights (specifying
the date on which the holders of Preferred Stock shall be entitled thereto) or
for determining rights to vote in respect of such Merger, dissolution,
liquidation or winding up; (B) in the case of any such Merger, dissolution,
liquidation or winding up, at least twenty (20) days' prior written notice of
the date when the same shall take place (and specifying the date on which the
holders of Preferred Stock shall be entitled to exchange their Preferred Stock
for securities or other property deliverable upon such Merger or any such
Reorganization, dissolution, liquidation or winding up); and (C) in the case of
a public offering, the Company shall give the Warrantholder at least twenty (20)
days written notice prior to the effective date thereof.

          Each such written notice shall set forth, in reasonable detail, (i)
the event requiring the adjustment, (ii) the amount of the adjustment, (iii) the
method by which such adjustment was calculated, (iv) the Exercise Price, and (v)
the number of shares subject to purchase hereunder after giving effect to such
adjustment, and shall be given by first class mail, postage prepaid, addressed
to the Warrantholder, at the address as shown on the books of the Company.

     (g)  Timely Notice.  Failure to timely provide such notice required by
          -------------
subsection (f) above shall entitle Warrantholder to retain the benefit of the
applicable notice period notwithstanding anything to the contrary contained in
any insufficient notice received by Warrantholder.  The notice period shall
begin on the date Warrantholder actually receives a written notice containing
all the information specified above.

9.   REPRESENTATIONS, WARRANTIES AND COVENANTS OF THE COMPANY.
     ---------------------------------------------------------

     (a)  Reservation of Preferred Stock.  The Preferred Stock issuable
          -------------------------------
upon exercise of the Warrantholder's rights has been duly and validly reserved
and, when issued in accordance with the provisions of this Warrant Agreement,
will be validly issued, fully paid and non-assessable, and will be free of any
taxes, liens, charges or encumbrances of any nature whatsoever; provided,
however, that the Preferred Stock issuable pursuant to this Warrant Agreement
may be subject to restrictions on transfer under state and/or Federal securities
laws.  The Company has made available to the Warrantholder true, correct and
complete copies of its Charter and Bylaws, as amended.  The issuance of
certificates for shares of Preferred Stock upon exercise of the Warrant
Agreement shall be made without charge to the Warrantholder for any issuance tax
in respect thereof, or other cost incurred by the Company in connection with
such exercise and the related issuance of shares of Preferred Stock.  The
Company shall not be required to pay any tax which

                                       6.
<PAGE>

may be payable in respect of any transfer involved and the issuance and delivery
of any certificate in a name other than that of the Warrantholder.

     (b)  Due Authority.  The execution and delivery by the Company of this
          -------------
Warrant Agreement and the performance of all obligations of the Company
hereunder, including the issuance to Warrantholder of the right to acquire the
shares of Preferred Stock, have been duly authorized by all necessary corporate
action on the part of the Company, and the Loans and this Warrant Agreement are
not inconsistent with the Company's Charter or Bylaws, do not contravene any law
or governmental rule, regulation or order applicable to it, do not and will not
contravene any provision of, or constitute a default under, any indenture,
mortgage, contract or other instrument to which it is a party or by which it is
bound, and the Loans and this Warrant Agreement constitute legal, valid and
binding agreements of the Company, enforceable in accordance with their
respective terms.

     (c)  Consents and Approvals. No consent or approval of, giving of notice
          ----------------------
to, registration with, or taking of any other action in respect of any state,
Federal or other governmental authority or agency is required with respect to
the execution, delivery and performance by the Company of its obligations under
this Warrant Agreement, except for the filing of notices pursuant to Regulation
D under the 1933 Act and any filing required by applicable state securities law,
which filings will be effective by the time required thereby.

     (d)  Issued Securities. All issued and outstanding shares of Common Stock,
          -----------------
Preferred Stock or any other securities of the Company have been duly authorized
and validly issued and are fully paid and nonassessable. All outstanding shares
of Common Stock, Preferred Stock and any other securities were issued in full
compliance with all Federal and state securities laws. In addition:

               (i)       The authorized capital of the Company consists of (A)
          10,000,000 shares of Common Stock, of which 2,807,145 shares are
          issued and outstanding, (B) 2,175,000 shares of Series A Preferred
          Stock, of which 2,175,000 shares are issued and outstanding and are
          convertible into 2,175,000 shares of Common Stock, (C) 3,825,000
          shares of Series B Preferred Stock, of which 3,424,365 shares are
          issued and outstanding and are convertible into 3,424,365 shares of
          Common Stock.

               (ii)      The Company has reserved (A) 765,000 shares of Common
          Stock for issuance under its 1997 Equity Incentive Plan, under which
          512,393 options are outstanding. There are no other options, warrants,
          conversion privileges or other rights presently outstanding to
          purchase or otherwise acquire any authorized but unissued shares of
          the Company's capital stock or other securities of the Company.

               (iii)  In accordance with the Company's Articles of
          Incorporation, no shareholder of the Company has preemptive rights to
          purchase new issuances of the Company's capital stock.

                                       7.
<PAGE>

          (e) Insurance.  The Company has in full force and effect insurance
              ---------
policies, with extended coverage, insuring the Company and its property and
business against such losses and risks, and in such amounts, as are customary
for corporations engaged in a similar business and similarly situated and as
otherwise may be required pursuant to the terms of any other contract or
agreement.

          (f) Other Commitments to Register Securities.  Except as set forth in
              ----------------------------------------
this Warrant Agreement, the Company is not, pursuant to the terms of any other
agreement currently in existence, under any obligation to register under the
1933 Act any of its presently outstanding securities or any of its securities
which may hereafter be issued.

          (g) Exempt Transaction.  Subject to the accuracy of the
              ------------------
Warrantholder's representations in Section 10 hereof, the issuance of the
Preferred Stock upon exercise of this Warrant will constitute a transaction
exempt from (i) the registration requirements of Section 5 of the 1933 Act, in
reliance upon Section 4(2) thereof, and (ii) the qualification requirements of
the applicable state securities laws.

          (h) Compliance with Rule 144.  At the written request of the
              ------------------------
Warrantholder, who proposes to sell Preferred Stock issuable upon the exercise
of the Warrant in compliance with Rule 144 promulgated by the Securities and
Exchange Commission, the Company shall furnish to the Warrantholder, within ten
days after receipt of such request, a written statement confirming the Company's
compliance with the filing requirements of the Securities and Exchange
Commission as set forth in such Rule, as such Rule may be amended from time to
time.

10.       REPRESENTATIONS AND COVENANTS OF THE WARRANTHOLDER.
          ---------------------------------------------------

          This Warrant Agreement has been entered into by the Company in
reliance upon the following representations and covenants of the Warrantholder:

          (a) Investment Purpose.  The right to acquire Preferred Stock or the
              ------------------
Preferred Stock issuable upon exercise of the Warrantholder's rights contained
herein will be acquired for investment and not with a view to the sale or
distribution of any part thereof, and the Warrantholder has no present intention
of selling or engaging in any public distribution of the same except pursuant to
a registration or exemption.

          (b) Private Issue.  The Warrantholder understands (i) that the
              -------------
Preferred Stock issuable upon exercise of this Warrant is not registered under
the 1933 Act or qualified under applicable state securities laws on the ground
that the issuance contemplated by this Warrant Agreement will be exempt from the
registration and qualifications requirements thereof, and (ii) that the
Company's reliance on such exemption is predicated on the representations set
forth in this Section 10.

          (c) Disposition of Warrantholder's Rights.  In no event will the
              -------------------------------------
Warrantholder make a disposition of any of its rights to acquire Preferred Stock
or Preferred Stock issuable upon exercise of such rights unless and until (i) it
shall have notified the Company of the proposed disposition, and (ii) if
requested by the Company, it shall have furnished the Company with an

                                       8.
<PAGE>

opinion of counsel (which counsel may either be inside or outside counsel to the
Warrantholder) satisfactory to the Company and its counsel to the effect that
(A) appropriate action necessary for compliance with the 1933 Act has been
taken, or (B) an exemption from the registration requirements of the 1933 Act is
available. Notwithstanding the foregoing, the restrictions imposed upon the
transferability of any of its rights to acquire Preferred Stock or Preferred
Stock issuable on the exercise of such rights do not apply to transfers from the
beneficial owner of any of the aforementioned securities to its nominee or from
such nominee to its beneficial owner, and shall terminate as to any particular
share of Preferred Stock when (1) such security shall have been effectively
registered under the 1933 Act and sold by the holder thereof in accordance with
such registration or (2) such security shall have been sold without registration
in compliance with Rule 144 under the 1933 Act, or (3) a letter shall have been
issued to the Warrantholder at its request by the staff of the Securities and
Exchange Commission or a ruling shall have been issued to the Warrantholder at
its request by such Commission stating that no action shall be recommended by
such staff or taken by such Commission, as the case may be, if such security is
transferred without registration under the 1933 Act in accordance with the
conditions set forth in such letter or ruling and such letter or ruling
specifies that no subsequent restrictions on transfer are required. Whenever the
restrictions imposed hereunder shall terminate, as hereinabove provided, the
Warrantholder or holder of a share of Preferred Stock then outstanding as to
which such restrictions have terminated shall be entitled to receive from the
Company, without expense to such holder, one or more new certificates for the
Warrant or for such shares of Preferred Stock not bearing any restrictive
legend.

     (d) Financial Risk.  The Warrantholder has such knowledge and experience
         --------------
in financial and business matters as to be capable of evaluating the merits and
risks of its investment, and has the ability to bear the economic risks of its
investment.

     (e) Risk of No Registration.  The Warrantholder understands that if the
         -----------------------
Company does not register with the Securities and Exchange Commission pursuant
to Section 12 of the 1934 Act (the "l934 Act"), or file reports pursuant to
Section 15(d), of the 1934 Act", or if a registration statement covering the
securities under the 1933 Act is not in effect when it desires to sell (i) the
rights to purchase Preferred Stock pursuant to this Warrant Agreement, or (ii)
the Preferred Stock issuable upon exercise of the right to purchase, it may be
required to hold such securities for an indefinite period. The Warrantholder
also understands that any sale of its rights of the Warrantholder to purchase
Preferred Stock or Preferred Stock which might be made by it in reliance upon
Rule 144 under the 1933 Act may be made only in accordance with the terms and
conditions of that Rule.

     (f) Accredited Investor.   Warrantholder is an "accredited investor" within
         -------------------
the meaning of the Securities and Exchange Rule 501 of Regulation D, as
presently in effect.

11.  TRANSFERS.
     ----------

          Subject to the terms and conditions contained in Section 10 hereof,
this Warrant Agreement and all rights hereunder are transferable in whole or in
part by the Warrantholder and any successor transferee, provided, however, in no
event shall the number of transfers of the rights and interests in all of the
Warrants exceed three (3) transfers.  The transfer shall be recorded on the
books of the Company upon receipt by the Company of a notice of transfer in the

                                       9.
<PAGE>

form attached hereto as Exhibit III (the "Transfer Notice"), at its principal
offices and the payment to the Company of all transfer taxes and other
governmental charges imposed on such transfer.

12.  MISCELLANEOUS.
     --------------

     (a)  Effective Date. The provisions of this Warrant Agreement shall be
          ---------------
construed and shall be given effect in all respects as if it had been executed
and delivered by the Company on the date hereof. This Warrant Agreement shall be
binding upon any successors or assigns of the Company.

     (b)  Attorney's Fees. In any litigation, arbitration or court proceeding
          ----------------
between the Company and the Warrantholder relating hereto, the prevailing party
shall be entitled to attorneys' fees and expenses and all costs of proceedings
incurred in enforcing this Warrant Agreement.

     (c)  Governing Law. This Warrant Agreement shall be governed by and
          -------------
construed for all purposes under and in accordance with the laws of the State of
California.

     (d)  Counterparts.  This Warrant Agreement may be executed in two or
          ------------
more counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

     (e)  Notices. Any notice required or permitted hereunder shall be given in
          -------
writing and shall be deemed effectively given upon personal delivery, facsimile
transmission (provided that the original is sent by personal delivery or mail as
hereinafter set forth) or seven (7) days after deposit in the United States
mail, by registered or certified mail, addressed (i) to the Warrantholder at
6111 North River Road, Rosemont, Illinois 60018, Attention: Venture Lease
Administration, cc: Legal Department, Attention: General Counsel, (and/or, if by
facsimile, (847) 518-5465 and (847)518-5088 and (ii) to the Company at 442
Potrero Ave., Sunnyvale, CA 94086, Attention: Chief Financial Officer (and/or if
by facsimile, (408) 738-7150) or at such other address as any such party may
subsequently designate by written notice to the other party.

     (f)  Remedies. In the event of any default hereunder, the non-defaulting
          --------
party may proceed to protect and enforce its rights either by suit in equity
and/or by action at law, including but not limited to an action for damages as a
result of any such default, and/or an action for specific performance for any
default where Warrantholder will not have an adequate remedy at law and where
damages will not be readily ascertainable. The Company expressly agrees that it
shall not oppose an application by the Warrantholder or any other person
entitled to the benefit of this Agreement requiring specific performance of any
or all provisions hereof or enjoining the Company from continuing to commit any
such breach of this Agreement.

     (g)  No Impairment of Rights. The Company will not, by amendment of its
          -----------------------
Charter or through any other means, avoid or seek to avoid the-observance or
performance of any of the terms of this Warrant, but will at all times in good
faith assist in the carrying out of all such terms and in the taking of all such
actions as may be necessary or appropriate in order to protect the rights of the
Warrantholder against impairment.

                                      10.
<PAGE>

     (h)  Survival. The representations, warranties, covenants and conditions of
          --------
the respective parties contained herein or made pursuant to this Warrant
Agreement shall survive the execution and delivery of this Warrant Agreement.

     (i)  Severability. In the event any one or more of the provisions of this
          ------------
Warrant Agreement shall for any reason be held invalid, illegal or
unenforceable, the remaining provisions of this Warrant Agreement shall be
unimpaired, and the invalid, illegal or unenforceable provision shall be
replaced by a mutually acceptable valid, legal and enforceable provision, which
comes closest to the intention of the parties underlying the invalid, illegal or
unenforceable provision.

     (j)  Amendments.  Any provision of this Warrant Agreement may be
          ----------
amended by a written instrument signed by the Company and by the Warrantholder.

          IN WITNESS WHEREOF, the parties hereto have caused this Warrant
Agreement to be executed by its officers thereunto duty authorized as of the
Effective Date.

                              Company:  ALIGN TECHNOLOGY INC.

                              By:____________________________

                              Title:_________________________
                                              CEO

                              Warrantholder: COMDISCO, INC.

                              By:____________________________
                                        JILL C. HANSES

                              Title:_________________________
                                      SENIOR VICE PRESIDENT

                                      11.
<PAGE>

                                   EXHIBIT I

                              NOTICE OF EXERCISE

TO:  ___________________________

(1)  The undersigned Warrantholder hereby elects to purchase _________ shares of
     the Series B Preferred Stock of ___________________, pursuant to the terms
     of the Warrant Agreement dated the _____ day of ______________, 19__ (the
     "Warrant Agreement") between ___________________________ and the
     Warrantholder, and tenders herewith payment of the purchase price for such
     shares in full, together with all applicable transfer taxes, if any.

(2)  In exercising its rights to purchase the Series B Preferred Stock of
     __________________________, the undersigned hereby confirms and
     acknowledges the investment representations and warranties made in Section
     10 of the Warrant Agreement.

(3)  Please issue a certificate or certificates representing said shares of
     Series 6 Preferred Stock in the name of the undersigned or in such other
     name as is specified below.

___________________________
(Name)

___________________________
(Address)

Warrantholder: COMDISCO, INC.

By: _________________________

Title: ______________________

Date:  ______________________

                                      12.
<PAGE>

                                  EXHIBIT II

                          ACKNOWLEDGMENT OF EXERCISE

     The undersigned ______________________________, hereby acknowledge receipt
of the "Notice of Exercise" from Comdisco, Inc., to purchase _____ shares of the
Series B Preferred Stock of _____________, pursuant to the terms of the Warrant
Agreement, and further acknowledges that _____ shares remain subject to purchase
under the terms of the Warrant Agreement.

                                        Company:

                                        By:___________________________

                                        Title:________________________

                                        Date:_________________________

                                      13.
<PAGE>

                                  EXHIBIT III

                                TRANSFER NOTICE

(To transfer or assign the foregoing Warrant Agreement execute this form and
supply required information.  Do not use this form to purchase shares.)

     FOR VALUE RECEIVED, the foregoing Warrant Agreement and all rights
evidenced thereby are hereby transferred and assigned to

_____________________________________
(Please Print)

whose address is_____________________

_____________________________________

              Dated:_____________________________

              Holders Signature: ________________

              Holder Address:    ________________

              __________________________________

Signature Guaranteed:____________________

NOTE:      The signature to this Transfer Notice must correspond with the name
           as it appears on the face of the Warrant Agreement, without
           alteration or enlargement or any change whatever. Officers of
           corporations and those acting in a fiduciary or other representative
           capacity should file proper evidence of authority to assign the
           foregoing Warrant Agreement.

                                      14.<PAGE>

                                                                   Exhibit 10.15

                             ALIGN TECHNOLOGY, INC.

                           INDEMNIFICATION AGREEMENT

          THIS INDEMNIFICATION AGREEMENT (this "Agreement") is made and entered
into this [Day] day of [MoYear] between Align Technology, Inc., a Delaware
corporation (the "Company"), and [Name] ("Indemnitee").

          WHEREAS, Indemnitee, a member of the Board of Directors, performs a
valuable service in such capacity for the Company;

          WHEREAS, the stockholders of the Company have adopted Bylaws (the
"Bylaws") providing for the indemnification of the officers, directors,
employees and agents of the Company to the maximum extent authorized by Section
145 of the Delaware General Corporation Law, as amended (the "Code");

          WHEREAS, the Bylaws and the Code, by their non-exclusive nature,
permit contracts between the Company and the members of its Board of Directors
with respect to indemnification of such directors;

          WHEREAS, in accordance with the authorization as provided by the Code,
the Company either has purchased and presently maintains or intends to purchase
and maintain a policy or policies of Directors Liability Insurance ("Directors'
Insurance") covering certain liabilities which may be incurred by its directors
in the performance of their duties as directors of the Company;

          WHEREAS, as a result of developments affecting the terms, scope and
availability of Directors' Insurance there exists general uncertainty as to the
extent of protection afforded members of the Board of Directors by such
Directors' Insurance and by statutory and bylaw indemnification provisions; and

          WHEREAS, in order to induce Indemnitee to continue to serve as a
member of the Board of Directors of the Company, the Company has determined and
agreed to enter into this contract with Indemnitee.

          NOW, THEREFORE, in consideration of Indemnitee's continued service as
a director after the date hereof, and for other good and valid consideration,
the receipt and adequacy of which is hereby acknowledged, the parties hereto
agree as follows:

          1.   Indemnification of Indemnitee.  The Company hereby agrees to hold
               -----------------------------
harmless and indemnify Indemnitee to the fullest extent authorized or permitted
by the provisions of the Code, as may be amended from time to time.

          2.   Additional Indemnity.  Subject only to the exclusions set forth
               --------------------
in Sections 3 and 6(c) hereof, the Company hereby further agrees to hold
harmless and indemnify Indemnitee:
<PAGE>

               (a)  against any and all expenses (including attorneys' fees),
witness fees, judgments, fines and amounts paid in settlement actually and
reasonably incurred by Indemnitee in connection with any threatened, pending or
completed action, suit or proceeding, whether civil, criminal, administrative or
investigative (including an action by or in the right of the Company) to which
Indemnitee is, was or at any time becomes a party, or is threatened to be made a
party, by reason of the fact that Indemnitee is, was or at any time becomes a
director of the Company or any subsidiary of the Company, or is or was serving
or at any time serves at the request of the Company as a director of another
corporation, partnership, joint venture, trust, employee benefit plan or other
enterprise; and

               (b)  otherwise to the fullest extent as may be provided to
Indemnitee by the Company under the non-exclusivity provisions of Article VII,
Section 6 of the Bylaws of the Company and the Code.

          3.   Limitations on Additional Indemnity.
               -----------------------------------

               (a)  No indemnity pursuant to Section 2 hereof shall be paid by
the Company:

                    i)     in respect to remuneration paid to Indemnitee if it
shall be determined by a final judgment or other final adjudication that such
remuneration was in violation of law;

                    ii)    on account of any suit in which judgment is rendered
against Indemnitee for an accounting of profits made from the purchase or sale
by Indemnitee of securities of the Company pursuant to the provisions of Section
16(b) of the Securities Exchange Act of 1934 and amendments thereto or similar
provisions of any federal, state or local statutory law;

                    iii)   on account of Indemnitee's conduct which is finally
adjudged to have been knowingly fraudulent or deliberately dishonest or to
constitute willful misconduct;

                    iv)    on account of Indemnitee's conduct which is the
subject of an action, suit or proceeding described in Section 6(c)(ii) hereof;

                    v)     on account of any action, claim or proceeding (other
than a proceeding referred to in Section 7(b) hereof) initiated by the
Indemnitee unless such action, claim or proceeding was authorized in the
specific case by action of the Board of Directors;

                    vi)    if a final decision by a Court having jurisdiction in
the matter shall determine that such indemnification is not lawful (and, in this
respect, both the Company and Indemnitee have been advised that the Securities
and Exchange Commission believes that indemnification for liabilities arising
under the federal securities laws is against public policy and is, therefore,
unenforceable and that claims for indemnification should be submitted to
appropriate courts for adjudication); and

                                       2
<PAGE>

                    vii)   except to the extent the aggregate of losses to be
indemnified thereunder exceeds the sum of (a) such losses for which the
Indemnitee is indemnified pursuant to Section 1 hereof and (b) any additional
amount paid to the Indemnitee pursuant to any Directors' Insurance purchased and
maintained by the Company.

               (b)  No indemnity pursuant to Section 1 or 2 hereof shall be paid
by the Company if the action, suit or proceeding with respect to which a claim
for indemnity hereunder is made arose from or is based upon any of the
following:

                    i)     Any solicitation of proxies by Indemnitee, or by a
group of which he was or became a member consisting of two or more persons that
had agreed (whether formally or informally and whether or not in writing) to act
together for the purpose of soliciting proxies, in opposition to any
solicitation of proxies approved by the Board of Directors.

                    ii)    Any activities by Indemnitee that constitute a breach
of or default under any agreement between Indemnitee and the Company.

          4.   Contribution.  If the indemnification provided in Sections 1 and
               ------------
2 hereof is unavailable by reason of a Court decision described in Section
3(a)(vi) hereof based on grounds other than any of those set forth in paragraphs
(i) through (v) of Section 3 (a) hereof, then in respect of any threatened,
pending or completed action, suit or proceeding in which the Company is jointly
liable with Indemnitee (or would be if joined in such action, suit or
proceeding), the Company shall contribute to the amount of expenses (including
attorneys' fees), judgments, fines and amounts paid in settlement actually and
reasonably incurred and paid or payable by Indemnitee in such proportion as is
appropriate to reflect (i) the relative benefits received by the Company on the
one hand and Indemnitee on the other hand from the transaction from which such
action, suit or proceeding arose, and (ii) the relative fault of the Company on
the one hand and of Indemnitee on the other in connection with the events which
resulted in such expenses, judgments, fines or settlement amounts, as well as
any other relevant equitable considerations. The relative fault of the Company
on the one hand and of Indemnitee on the other shall be determined by reference
to, among other things, the parties' relative intent, knowledge, access to
information and opportunity to correct or prevent the circumstances resulting in
such expenses, judgments, fines or settlement amounts. The Company agrees that
it would not be just and equitable if contribution pursuant to this Section 4
were determined by pro rata allocation or any other method of allocation which
does not take account of the foregoing equitable considerations.

          5.   Notification and Defense of Claim.  Not later than thirty (30)
               ---------------------------------
days after receipt by Indemnitee of notice of the commencement of any action,
suit or proceeding, Indemnitee shall, if a claim in respect thereof is to be
made against the Company under this Agreement, notify the Company of the
commencement thereof; but Indemnitee's omission so to notify the Company will
not relieve the Company from any liability which it may have to Indemnitee
otherwise than under this Agreement. With respect to any such action, suit or
proceeding as to which Indemnitee notifies the Company of the commencement
thereof:

                                       3
<PAGE>

               (a)  The Company will be entitled to participate therein at its
own expense.

               (b)  Except as otherwise provided below, to the extent that it
may wish, the Company shall, jointly with any other indemnifying party similarly
notified, be entitled to assume the defense thereof, with counsel reasonably
satisfactory to Indemnitee. After notice from the Company to Indemnitee of its
election to assume the defense thereof, the Company will not be liable to
Indemnitee under this Agreement for any legal or other expenses subsequently
incurred by Indemnitee in connection with the defense thereof, other than
reasonable costs of investigation or as otherwise provided below. Indemnitee
shall have the right to employ its own counsel in such action, suit or
proceeding, but the fees and expenses of such counsel incurred after notice from
the Company of the Company's assumption of the defense thereof shall be at the
expense of Indemnitee unless (i) the employment of counsel by Indemnitee has
been authorized by the Company; (ii) Indemnitee shall have reasonably concluded
that there may be a conflict of interest between the Company and Indemnitee in
the conduct of the defense of such action; or (iii) the Company shall not in
fact have employed counsel to assume the defense of such action; in each of
which cases the fees and expenses of Indemnitee's separate counsel shall be paid
by the Company. The Company shall not be entitled to assume the defense of any
action, suit or proceeding brought by or on behalf of the Company or as to which
Indemnitee shall have made the conclusion provided for in (ii) above.

               (c)  The Company shall not be liable to indemnify Indemnitee
under this Agreement for any amounts paid in settlement of any action or claim
effected without its written consent. The Company shall be permitted to settle
any action except that it shall not settle any action or claim in any manner
which would impose any penalty or limitation on Indemnitee without Indemnitee's
written consent. Neither the Company nor Indemnitee will unreasonably withhold
its consent to any proposed settlement.

          6.   Advancement and Repayment of Expenses.
               -------------------------------------

               (a)  In the event that Indemnitee employs his or her own counsel
pursuant to Sections 5(b)(i) through (iii) above, the Company shall advance to
Indemnitee, prior to any final disposition of any threatened or pending action,
suit or proceeding, whether civil, criminal, administrative or investigative,
any and all reasonable expenses (including legal fees and expenses) incurred in
investigating or defending any such action, suit or proceeding within ten (10)
days after receiving from Indemnitee copies of invoices presented to Indemnitee
for such expenses.

               (b)  Indemnitee agrees that Indemnitee will reimburse the Company
for all reasonable expenses paid by the Company in investigating or defending
any civil or criminal action, suit or proceeding against Indemnitee in the event
and only to the extent it shall be ultimately determined by a final judicial
decision (from which there is no right of appeal) that Indemnitee is not
entitled, under the provisions of the Code, the Bylaws, this Agreement or
otherwise, to be indemnified by the Company for such expenses.

               (c)  Notwithstanding the foregoing, the Company shall not be
required to advance such expenses to Indemnitee in respect of any action arising
from or based upon any

                                       4
<PAGE>

of the matters set forth in subsection (b) of Section 3 or if Indemnitee (i)
commences any action, suit or proceeding as a plaintiff unless such advance is
specifically approved by a majority of the Board of Directors or (ii) is a party
to an action, suit or proceeding brought by the Company and approved by a
majority of the Board which alleges willful misappropriation of corporate assets
by Indemnitee, disclosure of confidential information in violation of
Indemnitee's fiduciary or contractual obligations to the Company, or any other
willful and deliberate breach in bad faith of Indemnitee's duty to the Company
or its shareholders.

          7.   Enforcement.
               -----------

               (a)  The Company expressly confirms and agrees that it has
entered into this Agreement and assumed the obligations imposed on the Company
hereby in order to induce Indemnitee to continue as a directorof the Company,
and acknowledges that Indemnitee is relying upon this Agreement in continuing in
such capacity.

               (b)  In the event Indemnitee is required to bring any action to
enforce rights or to collect moneys due under this Agreement and is successful
in such action, the Company shall reimburse Indemnitee for all Indemnitee's
reasonable fees and expenses, including attorney's fees, in bringing and
pursuing such action.

          8.   Subrogation.  In the event of payment under this agreement, the
               -----------
Company shall be subrogated to the extent of such payment to all of the rights
of recovery of Indemnitee, who shall execute all documents required and shall do
all acts that may be necessary to secure such rights and to enable the Company
effectively to bring suit to enforce such rights.

          9.   Continuation of Obligations.  All agreements and obligations of
               ---------------------------
the Company contained herein shall commence upon the date that Indemnitee first
became a member of the Board of Directors of the Company, as the case may be,
and shall continue during the period Indemnitee is a director of the Company (or
is or was serving at the request of the Company as a director of another
corporation, partnership, joint venture, trust, employee benefit plan or other
enterprise) and shall continue thereafter so long as Indemnitee shall be subject
to any possible claim or threatened, pending or completed action, suit or
proceeding, whether civil, criminal or investigative, by reason of the fact that
Indemnitee was a director of the Company or serving in any other capacity
referred to herein.

          10.  Survival of Rights.  The rights conferred on Indemnitee by this
               ------------------
Agreement shall continue after Indemnitee has ceased to be a director of the
Company and shall inure to the benefit of Indemnitee's heirs, executors and
administrators.

          11.  Non-Exclusivity of Rights.  The rights conferred on Indemnitee by
               -------------------------
this Agreement shall not be exclusive of any other right which Indemnitee may
have or hereafter acquire under any statute, provision of the Company's
Certificate of Incorporation or Bylaws, agreement, vote of stockholders or
directors, or otherwise, both as to action in his official capacity and as to
action in another capacity while holding office; provided, however, that this
Agreement shall supersede and replace any prior indemnification agreements
entered into by and between the Company and Indemnitee and that any such prior
indemnification agreement shall be terminated upon the execution of this
Agreement.

                                       5
<PAGE>

          12.  Separability.  Each of the provisions of this Agreement is a
               ------------
separate and distinct agreement and independent of the others, so that if any or
all of the provisions hereof shall be held to be invalid or unenforceable for
any reason, such invalidity or unenforceability shall not affect the validity or
enforceability of the other provisions hereof or the obligation of the Company
to indemnify the Indemnitee to the full extent provided by the Bylaws or the
Code.

          13.  Governing Law.  This Agreement shall be interpreted and enforced
               -------------
in accordance with the laws of the State of Delaware.

          14.  Binding Effect.  This Agreement shall be binding upon Indemnitee
               --------------
and upon the Company, its successors and assigns, and shall inure to the benefit
of Indemnitee, his or her heirs, personal representatives and assigns and to the
benefit of the Company, its successors and assigns.

          15.  Amendment and Termination.  No amendment, modification,
               -------------------------
termination or cancellation of this Agreement shall be effective unless it is in
writing and is signed by both parties hereto.

          IN WITNESS WHEREOF, the parties hereto have executed this Agreement on
and as of the day and year first above written.

                              ALIGN TECHNOLOGY, INC.
                              a Delaware corporation

                              By:
                                  ----------------------------------------------

                              INDEMNITEE

                              --------------------------------------------------
                              [Name], [Title]

                      Address:
                              --------------------------------------------------

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

                                       6

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