PCT No. PCT/JP95/01897 Sec. 371 Date Mar. 19, 1997 Sec. 102(e) Date Mar. 19, 1997 PCT Filed Sep. 20, 1995A method of straightening a wire rod of titanium or titanium alloy wherein the rod is hot-straightened to a straight rod at the straightening temperature T and elongation epsilon satisfying the expression (1) or (2). The method includes hot rolling a titanium billet of beta titanium alloy, ( alpha + beta ) titanium alloy or a near alpha titanium alloy into a wire rod, winding the hot rolled wire rod into a coil, cold drawing the wire rod, cutting the wire rod to obtain a bent wire rod, heating the bent wire rod to a straightening temperature T while both end portions of the bent wire rod are fixed, applying a predetermined elongation epsilon to the wire rod, maintaining a straightening temperature T, hot-straightening the wire in accordance with the expression (2) epsilon (T-400)>/=400(1) epsilon (T-500)>/=200(2) and cooling the wire rod while applying tension. The method is suitable for preparing a straight rod for use in an engine valve.