A locking system that locks and unlocks a door of an elevator car travelling along a track having stopping points and associated stopping point zones includes a lock mechanism having a locking position wherein the door is immobilized in a closed position and an unlocking position wherein the door can be opened, an actuator for bringing the lock mechanism into the locking and unlocking positions, and a control device activating the actuator to bring the lock mechanism into the unlocking position when the car is located in the region of a stopping point zone. A position detecting unit continuously detects the position of the car relative to the track and communicates the position to the control device that continuously detects whether the car is located in the region of a stopping point zone by comparing the communicated car position to stored position limit values of the stopping point zones.