A method for screwing a ring nut of a trigger-shaped (5) pump or trigger (1) on a vessel (6), the pump or trigger being provided with a threaded fixing ring nut (2) by a gripping lever assembly (11). The method includes the steps of: screwing the ring nut on the threaded mouth of the vessel by screwing it to the body until the screwing torque does not reach a preset value; performing a first detachment of elements for tightening the ring nut; rotating the tightening elements (11), by an associated motor, relocating them in their starting configuration, by clearing the trigger by the presence of the levers (11) themselves; lastly, performing a further opening of the tightening elements from the ring nut (2); the driving being necessary for completely opening the gripper and clearing the trigger.