The invention concerns a radial tyre (1) comprising a crown, two beads (4) extended by sidewalls (2) including a radial carcass reinforcement (5), said carcass reinforcement (5) extending in the crown and anchored in each bead (4) to least one element (41) inextensible in the circumferential direction, said tyre (1) comprising, in at least one sidewall (2), an additional reinforcement ply (6) made of gum and reinforcing elements inclined relative to the circumferential direction. The invention is characterised in that, viewed in meridian cross-section: the additional reinforcement ply (6) comprises at least an assembly (61, 62) of at least two strips (61A, 61B, 61C, 61D, 62A, 62B, 62C, 62D) extending in the circumferential direction, each strip (61A, 61B, 61C, 61D, 62A, 62B, 62C, 62D), of width Li substantially equal or greater than the total width Lt of the reinforcement divided by the total number of strips in the assembly concerned, is formed of gum reinforced by a plurality of cords or yarns sloping at an angle alpha ranging between 30 DEG and 90 DEG , in one single common assembly, each circumferential strip is partly superimposed with a neighbouring strip.