A thrust reverser for a nacelle of an aircraft turbojet engine includes at least one movable thrust reverser cowl, a means for locking the cowl, a variable section outlet nozzle, and at least one actuator including an actuator rod. The thrust reverser is provided with a resilient coupler comprising a body which is rigidly connected to the thrust reverser cowl and a resilient return and abutment device that engages with the actuating rod of the actuator such as to resiliently return the nozzle to a neutral position. The return device is calibrated such that, when the cowl is unlocked, the return device opposes the relative movement of the actuating rod relative to the cowl, such as to enable the movement of the cowl and the nozzle, and when the cover is locked, the actuator drives the actuating rod against the return device to enable the movement of the nozzle.