A method for machining a toothing of a workpiece held in a clamping, in which a toothing tool that rotates about its rotational axis and comprises cutting edges is brought into rolling chip-removing machining engagement with the toothing that rotates about its rotational axis, in order to produce a predetermined tooth flank end geometry in one or more machining passes, wherein during the machining pass which produces the tooth flank end geometry, monitoring responsive to the event of a removed chip being pressed into a machined tooth flank of the toothing by means of the rolling machining process is carried out and, if the monitoring responds, an additional toothing machining process that removes the material protrusion on top of the tooth flank end geometry formed by the chip that was pressed in is implemented automatically, which process is carried out in the same clamping of the workpiece and by means of the toothing tool.