A method of assembling a member made of a first material in a part made of a second material having no plastic domain, including forming the part with an aperture; inserting an intermediate part, which is made of a third material and includes a hole into the aperture without any stress; introducing the member into the hole without any stress; elastically and plastically deforming the intermediate part by moving two tools towards each other axially, respectively on the top and bottom parts of the intermediate part, so as to exert a radial stress against the member and against the wall of the part surrounding the aperture by causing the elastic deformation of the part, in order to secure the assembly in a manner that is not destructive for the part. The member can be a time piece.