An assembly comprising a tire (P) without an inner tube, provided with two beads and intended to be mounted on a mounting rim (J) comprising seats (440) extended radially towards the outside by flanges (R), and a rubber sealing piece (E) arranged between said rim and said tire, characterized in that the diameters (DP) of the tire bead seats are greater than the corresponding diameters (DJ) of the rim seats (440), said tire (P) being provided integrally with the sealing piece (E) formed of three parts which are integral with each other, a central part (51), made of material impermeable to the inflation gases, being placed axially between the beads of the tire, this central part (51) being extended axially beneath the beads of the tire by edges (50) integral with said beads, means being provided for facilitating the separation of the central part from the lateral parts.A process for manufacturing such an assembly.