In a wire electric discharge machine in which chuck part electrodes that hold a wire electrode are provided on the upper side of an upper wire guide and electrodes of a detecting part are provided on a lower stream side of the chuck part electrodes, a part, which contacts with the chuck part electrodes, of a surface of the wire electrode is hardened by locally cooling down the part by air blowing during energization to the wire electrode. Accordingly, wire metal powder is hardly generated from the wire electrode even though the wire electrode rubs against the chuck part electrodes.