In order to achieve a long service life for a machining tool, in particular for a solid carbide drill, it is provided with a special wear protection coating. In a first method step, in order to form this coating, a first layer made of a first material is applied in the region of a cutting edge and in the adjoining surface regions, and specifically, a flank face and a rake face. In a second step, the applied first material of the first layer is selectively removed at least partially, and preferably completely, only in the region of the cutting edge. Finally, in a third method step, a second layer made of a second wear-resistant material is applied both to the cutting edge and to the face regions. In this way, a coating having a high overall thickness in the face regions is made possible, without the risk of cracking.