A tire with radial carcass reinforcement having two beads, the carcass reinforcement extending from one bead to the other, each bead having no anchoring bead wire and being reinforced by an armature including at least two plies (2) and (3) turned up over themselves to form four reinforcement layers (21, 31, 32, 22) axially close to one another, the two axially innermost layers (21, 31) being composed of elements parallel to one another from one layer (21) to the next (31), and the two layers (31, 32) axially at the center of the reinforcement being composed of elements crossed from one layer (31) to the next (32), such that the said elements make with the circumferential direction an angle null such that 0null