The invention concerns a radial body armour (1) with two beads B, said body armour (1) extending from one bead B to the next, each bead being devoid of anchoring bead core and reinforced by an armour R comprising at least two plies (2 and 3) folded back on themselves to form four reinforcing layers (21, 31, 32, 22) axially close to one another, the two axially innermost layers (21, 31) consisting of mutually parallel elements from one layer (21) to the next (31), and the two layers axially at the armour centre consist of elements crossed from one layer (31) to the next (32), said elements forming with the circumferential direction an angle α such that 0° α ≤ 10°, and the reinforcing layers (21, 22, 31, 32) having their radially outer ends arranged in the bead B at different heights H21, H22, H31,H32 such that every annular strip of the reinforcing armour R of the bead B, comprising at least two layers of reinforcing elements and included between the two tyre parallels, is formed by at least two layers of reinforcing elements crossed from one layer to the next.
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