Adapter providing the connection between one tire bead and the rim. An axially inner end of the adapter is mounted on the rim seat, an axially outer end is mounted on the rim seat, a body connects said outer end to said inner end, a substantially cylindrical adapter seat receives one of said beads, and an adapter bearing face is substantially contained in a plane perpendicular to the axis. The reinforcer element of the axially outer end is entirely situated axially outside the bearing face. The body comprises, opposite the adapter seat, an annular seat protuberance, said protuberance comprising at least one rubber composition.