A wire electrical discharge machine which has a workpiece plate thickness change detection part (120; 14) configured to detect a change of a plate thickness in a step portion of a workpiece based on energy applied from a power source unit (121; 1) for machining, and machines the workpiece by relatively moving a wire electrode with respect to the workpiece with electrical discharge generated, from the power source unit for machining, between the wire electrode and the workpiece, the wire electrical discharge machine comprising: a setting part configured to set a wire electrode inclination starting position located anterior to a step portion; and a wire electrode inclination starting position passing judgment part configured to determine whether or not the wire electrode passes the wire electrode inclination starting position set by the setting part; characterised by further comprising a wire electrode inclination control part configured to carry out control of inclining the wire electrode within the machining plane with respect to a side where the machining plane, formed by relative movement of the wire electrode with respect to the workpiece, crosses the surface of the step portion of the workpiece when the wire electrode inclination starting position passing judgment part determined that the wire electrode has passed the wire electrode inclination starting position; a step passing determination part configured to determine that the wire electrode has passed a position of the step portion when the plate thickness change detected by the workpiece plate thickness change detection part exceeds a preset value; and a wire electrode inclination finishing control part configured to finish the control of inclining the wire electrode when the step passing determination part determines that the wire electrode has passed the position of the step portion. a setting part configured to set a wire electrode inclination starting position located anterior to a step portion; and a wire electrode inclination starting position passing judgment part configured to determine whether or not the wire electrode passes the wire electrode inclination starting position set by the setting part; characterised by further comprising a wire electrode inclination control part configured to carry out control of inclining the wire electrode within the machining plane with respect to a side where the machining plane, formed by relative movement of the wire electrode with respect to the workpiece, crosses the surface of the step portion of the workpiece when the wire electrode inclination starting position passing judgment part determined that the wire electrode has passed the wire electrode inclination starting position; a step passing determination part configured to determine that the wire electrode has passed a position of the step portion when the plate thickness change detected by the workpiece plate thickness change detection part exceeds a preset value; and a wire electrode inclination finishing control part configured to finish the control of inclining the wire electrode when the step passing determination part determines that the wire electrode has passed the position of the step portion.