The bead wire (52) comprises several windings of wire and a basic hexagonal bead wire (56) comprising: two axially and radially external lateral rows (F1, F2) of N2 windings, two axially external and radially internal lateral rows (F3, F4) of N2 windings, where N1=N2+1 or N1=N2, two junctions (J1, J2), each formed by a winding that an axially and radially external lateral row (F1, F2) and an axially external and radially internal lateral row (F3, F4), have in common, each winding in common having no winding of wire axially on the outside of it. The bead wire (52) comprises two axially and radially external additional lateral rows (A1, A2) of N3 windings substantially parallel respectively to each axially and radially external lateral row (F1, F2).