Abstract: A machining method and apparatus for avoiding the double machining by a wire electrode of the same point on the desired contour of a workpiece, particularly the point where a predetermined entrance line intersects with the desired contour. The predetermined entrance line locus is automatically modified on the basis of the parameters of the workpiece and electrode such that at least a portion of the modified entrance line locus intersects the desired contour at an obtuse angle or a tangent, that portion of the modified locus being a curve or a straight line. The return locus from the desired contour to the entrance line also may be modified in addition or instead of the entrance line. The electrical parameters of the machining may further be monitored and modified in order to avoid intrusions of the desired contour.