In a method of welding a cut-out part with a workpiece at a preselected area in a thickness direction of the workpiece in a wire electrical discharge machining to retain temporarily or tentatively the part on the workpiece, a wire electrode 5 tilted in posture cuts the workpiece 6 to form a slant cutting surface 30 at a spark discharge location in a desired contour 21 in the workpiece 6. The wire electrode 5 after kept in an upright posture executes the welding process on the workpiece 6 along the slant cutting surface. A plurality of the welded spots is formed over a preselected length at preselected areas in the thickness direction of the workpiece 6. Even if the cut-out part 26 weighs more or the spark discharge is executed on the workpiece 6 overlapped one on the other, the welding spot 20 is formed in the thickness direction of the workpiece 6 adequately depending on the working situation to tentatively retain the cut-out part 26 on the workpiece 6.