A tool for machining a wall of a workpiece, made from a composite material, that can cut a groove in the wall, the tool including a head mounted integrally with a rod having a longitudinal axis and capable of being driven in rotation about the longitudinal axis. The head includes at least one main protruding annular rib with an outer surface covered with abrasive grains of predetermined particle size and with a radial height corresponding to the depth of the groove to be cut, and at least one auxiliary protruding annular rib with an outer surface covered with abrasive grains of predetermined particle size and with a radial height less than the radial height of a main rib. The auxiliary rib includes two circular ridges separated by a ring band that is flat and that can be conical in shape.