To provide a lock which allows a lock box and a cylinder lock to be arbitrarily selected for firm and reliable integration even if the lock box and the cylinder lock are different in specification, can extensively adapt to the thickness of the door, whereto the lock is applied, and has a high degree of safety against crimes.

A supporting cylinder is interposed between the lock box and the cylinder lock, the end of the cylinder lock is inserted into the supporting cylinder fixed to the lock box, and the supporting cylinder and the cylinder lock are fixed to each other so as to make the cylinder lock, which is out of specification or manufactured by different manufacturers, fixed to the arbitrary lock box. In addition, a covering cylinder for covering the end of the cylinder lock is installed protrusively in a face plate, which is fixed to the backside plate of the lock box for the purpose of providing the rim lock capable of adapting to the thicknesses of the various doors.