A tire has a carcass reinforcement extending between a pair of opposing bead portions. At least one of the bead portions terminates axially to the outside by a tip and is intended to be mounted on a wheel rim having a bead seat that has an axially outer end closer to the axis of rotation than the axially inner end thereof. Within the bead portion is a bead ring. The radial carcass reinforcement ply is anchored in each bead portion and has at least one terminal end located in the bead portions. In the bead portion, the reinforcement ply passes radially inward of the bead ring and along the axially outer side of an adjacent rubber component and terminates at a terminal end. The terminal end is axially spaced from the downturn portion of the ply, preferably the axial spacing is equal to or greater than the bead width.