A threading die (100) for cold-drawing a metal wire (4) is described; the threading die comprises a hole (103) for the inlet of the wire to be drawn and the hole comprises a conical part (106) for drawing the metal wire and a truncated-cone shaped part (105) which precedes the conical part in the advance path of the metal wire and wherein no decrease in the diameter of the metal wire occurs; the base with the greater diameter (111) of the truncated-cone shaped part precedes the base with the shorter diameter (112) in the advance path of the metal wire.