Tyre intended to be mounted on a mounting rim of a vehicle wheel, comprising: two beads, each bead comprising at least one anchoring zone and a portion forming a seat adapted to come into contact with the mounting rim; two sidewalls extending the beads radially outwards, the two sidewalls joining together to form a crown comprising a crown reinforcement (80, 90) surmounted by a tread; at least one carcass reinforcement (60, 62) extending from each of said two beads through the sidewall as far as the crown, the carcass reinforcement being anchored in the anchoring zone of the bead; wherein, in any radial cross section, the anchoring zone of each bead comprises a plurality of annular reinforcing structures, said annular reinforcing structures being arranged in such a way as to form at least one anchoring alignment (71, 72, 73), said at least one anchoring alignment extending over a length LT between a radially innermost annular reinforcing structure and a radially outermost annular reinforcing structure, along a trajectory that is parallel to a portion of the carcass reinforcement, each of said two beads further comprising, in any radial cross section, an additional stiffening reinforcement, the additional stiffening reinforcement extending between: (a) a first end situated at a distance H1 from a tangent to said portion forming a seat, the distance H1 being greater than or equal to 20% and less than or equal to 70% of the minimum distance H0 between: (i) the annular reinforcing structure of said at least one anchoring alignement that is closest to the tangent to said portion forming a seat, and (ii) the tangent to said portion forming a seat, the distances H1 and H0 being measured perpendicular to said tangent, the first end lying an axial distance L1 from the interior surface of the tyre, the axial distance L1 being greater than or equal to 50% and less than or equal to 85% of a maximum axial width L0 of the bead; and (b) a second end, the second end being radially at the same level as or outside of the first end and axially at the same level as or on the outside of the first end, the second end being chosen such that: a straight line connecting the first end and the second end forms an angle α (alpha) with the radial direction, the angle α (alpha) being greater than or equal to 0° and less than or equal to 90°; and wherein a distance LA separates the first end and the second end, the distance LA being greater than or equal to 30% of a mean length of the at least one anchoring alignment of annular reinforcing structures, and wherein the additional stiffening reinforcement is formed by one single alignment of at least two annular reinforcing structures. two beads, each bead comprising at least one anchoring zone and a portion forming a seat adapted to come into contact with the mounting rim; two sidewalls extending the beads radially outwards, the two sidewalls joining together to form a crown comprising a crown reinforcement (80, 90) surmounted by a tread; at least one carcass reinforcement (60, 62) extending from each of said two beads through the sidewall as far as the crown, the carcass reinforcement being anchored in the anchoring zone of the bead; (a) a first end situated at a distance H1 from a tangent to said portion forming a seat, the distance H1 being greater than or equal to 20% and less than or equal to 70% of the minimum distance H0 between: (i) the annular reinforcing structure of said at least one anchoring alignement that is closest to the tangent to said portion forming a seat, and (ii) the tangent to said portion forming a seat, the distances H1 and H0 being measured perpendicular to said tangent, the first end lying an axial distance L1 from the interior surface of the tyre, the axial distance L1 being greater than or equal to 50% and less than or equal to 85% of a maximum axial width L0 of the bead; and (i) the annular reinforcing structure of said at least one anchoring alignement that is closest to the tangent to said portion forming a seat, and (ii) the tangent to said portion forming a seat, (b) a second end, the second end being radially at the same level as or outside of the first end and axially at the same level as or on the outside of the first end, the second end being chosen such that: a straight line connecting the first end and the second end forms an angle α (alpha) with the radial direction, the angle α (alpha) being greater than or equal to 0° and less than or equal to 90°; and wherein a distance LA separates the first end and the second end, the distance LA being greater than or equal to 30% of a mean length of the at least one anchoring alignment of annular reinforcing structures, and wherein the additional stiffening reinforcement is formed by one single alignment of at least two annular reinforcing structures.