High-speed wire electrochemical-discharge cutting method (HS-WECDM), in which a work piece is processed by means of a wire electrode, in which consecutive negative polarity pulses are applied at said wire electrode, thereby at least partially developing discrete electrical discharges, wherein the method further includes, applying positive polarity pulses at the wire electrode between the negative pulses, and that an ignition occurring with each positive polarity pulse is immediately detected, and that the positive polarity pulses are immediately interrupted.