A disengageable cylinder for a motor vehicle lock mechanism includes a fixed stator, a sleeve, a rotor, a driver, and an indexer. The sleeve is mounted in rotation about its axis in the stator, and is fixed axially with respect to the stator. The rotor is mounted in rotation in the sleeve and is fixed axially in the sleeve. Further, the rotor includes tumblers which can move radially under the action of a key intended to be inserted axially into the rotor. The driver provides a coupling between the rotor and a cam actuator, when the key is appropriate. The indexer can move axially between rest and disengagement positions and is under the effect of a rotation of the sleeve with respect to the stator subsequent to the rotor being rotated by means of an inappropriate key.