Cadillac 2007 STS Owner's Manual page 92

The procedure will require three, ten minute cycles
to complete the matching process. Do the following:
1. The vehicle must be off.
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2. Place the new, unrecognized transmitter into
the transmitter pocket with the transmitter
buttons facing the front of the vehicle.
The transmitter pocket is inside the center
console storage area located between
the driver and front passenger seats.
3. Insert the vehicle key into the key lock
cylinder located on the driver's door.