For creating flat surfaces along the circumference of a polymer optical fiber of a round cross section by machining, the polymer optical fiber is wound onto a mandrel in a plurality of windings, the mandrel having a generally non-circular cross section with at least one projecting sector in which the radius is constant or, starting from an apex of the largest radius, in which the radius linearly decreases on both sides with an increasing angular distance to the apex, the machining including using a cutting chisel of a high quality for turning-off the polymer optical fiber in the projecting sector of the mandrel. Subsequently, the polymer optical fiber is cut to several pieces that can be used for the manufacture of optical splitters.