Exhibit 10.4

RIDER I

Rider to the lease dated 1 July 2004, entered into between Align Technology B.V. and Stichting Philips Pensioenfonds, currently TT Amsterdam Project Company Ltd, concerning office space comprising approx. 1.066 square meters, locally known as the ground floor and first floor of the building Telepsy at Arlandaweg 161, (1043 HR) Amsterdam the Netherlands (the “Existing  Lease”).

This Rider is hereby executed by and between:

Align Technology B.V., established in Amsterdam (1043 HR) at Arlandaweg 161,  in this matter duly represented by Mr T. Prescott and Mr. E. Bullington,

listed in the Commercial Register in Amsterdam under number 34207531

hereinafter referred to as the “Lessee”,

and

TT Amsterdam Project Company Ltd. c/o Padget-Brown Trust Company Ltd, established in West Wind Building, Harbour Drive, P.O. Box 1111, at George Town, Grand Cayman, British West Indies

in this matter duly represented by Mr H.D. Garrison,

listed in the Commercial Register under number PB-168944

hereinafter referred to as the “Lessor”

WHEREAS:

·The Lessee and the Lessor have agreed on the extension of the leased premises to include part of the second floor of the building of Telepsy, 3 parking spaces and a new lease term for a period of 5 years with a renewable 5 year option.

·The Lessee and the Lessor wish to lay down the agreements made regarding this extension and new term in writing.

THE PARTIES HAVE AGREED TO THE FOLLOWING:

Extension accommodation and new term

1.The lease term of the Existing Lease is hereby amended to include a 5 year term commencing on 1 June 2007 (the “ New Lease Term Commencement Date”) with an option to renew for an additional term of 5 years.

2.On the New Lease Term Commencement Date,  the leased premises referred to in Clause 3.1 of the Existing Lease shall be amended to include a part of the second floor and 3 additional parking spaces such that the total leased premises shall comprise approximately 1.526 m2 and 13 parking spaces.

Initials of the Lessor Initials of the Lessee

Conditions

Lease notice period:

The notice period referred to in Clause 3.3 of the Existing Lease shall be amended to include a 12 (twelve) month notice period.

The total leased property:

The total leased property shall comprise approximately 1.526 m2 of office space located on (i) the ground floor (487m2), (ii) on the first floor (579 m2) and (iii) part of the second floor (460m2) according to the NEN 2580, as well as 13 parking spaces.

The Rent amount provided Pursuant to Clause 4.1 of the Existing Lease shall be

amended as follows:

Current office space:	€ 204,- excl. of VAT
(current rent)
Extension office space (460 m²):	€ 180,- excl. of VAT
Parking spaces:	€ 1.514,- excl. of VAT
(current rent)

Creditable advance on service charges:

EUR 22 per m2, excl. of VAT. The service charges are invoiced quarterly in advance. Amounts paid are set off annually based on the costs actually incurred.

Rent-free period

Tenant will receive a rent-free period (excl. service charges) for the leased property of the extension office spaces (460 m2, second floor) and the 3 parking spaces for 1 ½ years (from 1 june 2007 until 1 December 2008).

State of delivery

The office space will be delivered in its current condition, with new carpet.

Right of first refusal
The lessee has a right of first refusal on the remaining office space on the 2nd, 3rd and 4th floors. If another party shows an interest in the remaining office space, the lessee will be notified in the form of a written offer (sent by registered post). Within 5 working days of receipt of this notification, the lessee will indicate by means of a letter sent by registered post whether it accepts the offer. If the lessee does not wish to accept the offer, or does not respond before the set deadline, the lessor will be free to let the space to third parties subject to conditions that the lessor itself will specify in so far as not determined otherwise in this agreement.

Remaining conditions present lease contract

All the remaining conditions of the Existing Lease contract which has not been laid down in this proposal don’t change and will be remain effective.

Initials of the Lessor Initials of the Lessee

Acceptance

Upon signature of the lease. The remaining time until the New Lease Term Commencement Date may be used to furnish the extension of the leased property.

Miscellaneous

Unless otherwise agreed in this rider, the provisions of the Existing Lease shall remain in full force and effect.

Signed, sealed and delivered in three copies.

August 3, 2007	August 3, 2007
p.p. the Lessor:	p.p. the Lessee:
(signature)	(signature)
/s/ Jeffrey D. Haroldson	/s/ T. Prescott
	(signature)
	/s/ Eldon M. Bullington