A process for drawing a steel wire, in which the wire has a carbon content by weight C of 0.4%≦C≦0.74%, includes an uninterrupted series of drawing steps. The drawing steps draw the wire from a diameter d′ to a diameter d, with d′ and d being expressed in mm, and with a true strain ε′ of the steel wire being given by ε′=2×ln(d′/d), with ε′>4.