Abstract: The system includes a direct-current voltage supply, an electric starter motor for rotating a movable pinion, and an electromagnetic operating device which, when it receives an excitation current, moves the pinion to couple it for rotation with a rotary member of the internal combustion engine. In operation, an electronic control unit cuts off the current supply to the electromagnetic operating device as soon as the speed of rotation of the engine shaft exceeds a predetermined threshold and the acceleration of the shaft is less than or equal to zero.