Abstract: To eliminate short-circuits between a countersink electrode and a workpiece during countersink erosion, when a short-circuit occurs, the countersink electrode is initially moved back by a predetermined path length (.delta.) along the previously travelled path from a first locus (P.sub.K) at which the short-circuit occurred to a second locus or intermediate point (P.sub.R) and it is established at that location whether there is still a short-circuit. If this is the case, the countersink electrode is moved in an upwardly sloping manner along a second path (R), which has a first angle (.alpha.) with respect to the working plane (AE) and has a movement component (R.sub.1) having a second angle (.beta.) with respect to a surface normal to the short-circuit or intermediate point (P.sub.K or P.sub.R). All the parameters (.alpha.,.beta.,.delta.,.vertline.R.vertline.) can be freely preselected and are variable during erosion.