A system for fastening a dispensing pump on the neck of a bottle containing a fluid product, the system including a sleeve having an interior collar for fastening of the pump and a lower skirt provided with fasteners for fastening the sleeve on the bottle, the system further including a hoop slidably mounted around the skirt between a top position wherein the fasteners are free and a bottom position wherein the fasteners are constrained by the hoop, the system further including an exterior collar mounted around the interior collar by the intermediary of a device for displacing the exterior collar between a bottom usage position and a top dismounting position, the hoop at the bottom position being attached to the exterior collar in order to actuate the displacement of the collar towards its top position by driving the hoop relatively to the skirt on a stroke that is sufficient to release the fasteners.