The machine has a rotary device for holding and rotating a workpiece to be processed, an electrode disposed to oppose the workpiece, an indexing device for holding the electrode and indexing the electrode at a predetermined angular pitch, a power supply device for applying a voltage between the workpiece and the electrode so as to cause the electric discharge therebetween, and a cutting device for cutting a portion of the electrode which has been used for the electric discharge and has been indexed by the indexing device to face the cutting device. The consumed portions of the electrode are successively indexed to the position where the cutting device is set so that the consumed portion of the electrode is successively cut without requiring the processing to be stopped.