A method of operating with a rivet is for the coupling and the tack riveting together of a first element and a second element. The method comprises positioning the rivet such that the rivet traverses two substantially coaxial openings arranged in the first and second elements to be assembled; pulling the mandrel to form a bulb on the second end; and resuming pulling of the mandrel, to cause a rupture of the sleeve at the bulb so as to permit removal, by way of the external surface of the first element, of the mandrel and of a first portion of the sleeve as well as the falling away of the portion of the bulb remaining on the external surface of the second element.