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A tire (1) comprising, viewed in meridian section, two beads (12) with generatrices which are inclined towards the outside, the upturn (130) of said reinforcement (13) being formed by the lateral (30) and radially inner (32) sides of a wedge-shaped profiled element (3) of high Shore A hardness and having an end located firstly axially to the outside of a straight line P2perpendicular to the axis of rotation and passing through the center of gravity of the annular anchoring element (14) and secondly axially to the inside and radially to the outside of the straight line P1passing through said center of gravity and forming with the axis of rotation an angle of between 30° and 60°, and the ratio e1/e2of the thickness e1between the carcass reinforcement upturn (130) and the annular anchoring element (14) to the thickness e2between the carcass reinforcement upturn (130) and the outer wall of the bead, measured on the straight line P1, satisfying the relationship:
0.05≦e1/e2<1.0.