A wire electrical discharge machine for detecting an end face of an object, configured so that when a contact detection movement is started and if contact between the wire electrode and the workpiece is detected, positions in which the contact between the wire electrode and the workpiece is detected are stored as contact detection positions and that when a non-contact detection movement is then started and if non-contact between the wire electrode and the workpiece is detected, positions in which the non-contact between the wire electrode and the workpiece is detected are stored as non-contact detection positions. When it is determined whether or not a set number of times of execution is reached and if the set number of times of execution is reached, a reference position is obtained by adding the radius of the wire electrode and a clearance of the wire guide to an end face determination position.