A wire electrical discharge machine (12, 12A to 12C) using a machining power source to apply a machining current across an electrode gap formed between a wire electrode and a workpiece to be machined and thereby perform electrical discharge machining on the workpiece, comprising: an electrode unit configured to supply the machining current to the electrode gap; a switch configured to change impedance between the machining power source and the electrode unit; characterised by a controller configured to, at a time of a core retaining process, turn off the switch so that the impedance is higher than the impedance in a cutting process and thereby suppress the machining current flowing through the electrode gap, wherein: the electrode unit includes a first electrode part connected to the wire electrode and a second electrode part connected to the workpiece, a first current supply line is connected to the machining power source and the first electrode part, a second current supply line is connected to the machining power source and the second electrode part, wherein: the first current supply line branches into a plurality of current lines each connected to the first electrode part and the switch is disposed on at least one of the plurality of branched current lines of the first current supply line; or the second current supply line branches into a plurality of current lines each connected to the second electrode part and the switch is disposed on at least one of the plurality of branched current lines of the second current supply line. an electrode unit configured to supply the machining current to the electrode gap; a switch configured to change impedance between the machining power source and the electrode unit; characterised by a controller configured to, at a time of a core retaining process, turn off the switch so that the impedance is higher than the impedance in a cutting process and thereby suppress the machining current flowing through the electrode gap, the electrode unit includes a first electrode part connected to the wire electrode and a second electrode part connected to the workpiece, a first current supply line is connected to the machining power source and the first electrode part, a second current supply line is connected to the machining power source and the second electrode part, wherein: the first current supply line branches into a plurality of current lines each connected to the first electrode part and the switch is disposed on at least one of the plurality of branched current lines of the first current supply line; or the second current supply line branches into a plurality of current lines each connected to the second electrode part and the switch is disposed on at least one of the plurality of branched current lines of the second current supply line. the first current supply line branches into a plurality of current lines each connected to the first electrode part and the switch is disposed on at least one of the plurality of branched current lines of the first current supply line; or the second current supply line branches into a plurality of current lines each connected to the second electrode part and the switch is disposed on at least one of the plurality of branched current lines of the second current supply line.