Embodiments disclosed herein provide a method of implanting an intervertebral disk prosthesis that can be assembled and disassembled in a minimally invasive fashion. The prosthesis comprises a first fixing element having an anchoring first face and a co-operation second face; a second fixing element having an anchoring first face and a co-operation second face; a first prosthesis element having an active first face and a co-operation second face, the co-operation faces of the first fixing element and the first prosthesis element serving to fasten the two elements together; a second prosthesis element having an active first face and a co-operation second face, the co-operation faces of the second fixing element and the second prosthesis element serving to fasten the two elements together; and each of the active faces of the prosthesis elements defining at least a portion of a spherical cap that is respectively concave or convex.