The invention relates to a method for making a rivet (R), of the type comprising, by deformation of the material of a substantially cylindrical metal segment, the operations of preforming a milled head (100) at the end of a rod (200), characterised in that it comprises, by deformation of the material (cold stamping) the following operations: creating a portion with a lower diameter (210) from the free end; creating a substantially cylindrical hollow core (220) for forming a tubular portion; preforming the hollow core (220) as a truncated cone; performing the lower diameter outer surface as a truncated cone. The invention also relates to the rivet obtained by said method.