The system includes a mode switching unit which switches the antitheft system into a code switching mode. Codes are registered in a storing unit and can be changed in the code switching mode when a code checking unit reads in at least two different first codes which are assigned to ignition keys (1a). The first codes have a determined relation to the second codes in the storing unit. The first code which is transmitted using a transponder (1) located in the key is temporary stored in a temporary storage unit. A register control unit controls the storage of at lest two first codes in the storage unit when the temporary storage unit is ready to store the first codes.
