A method and apparatus for the laser machining of an unfinished object into a cutting tool with a cutting edge and a free surface. A laser generates laser beam impulses which are directed by a redirecting arrangement onto a surface of the unfinished object. An impulse reaches an impact location on the surface of the unfinished object under an inclination angle between the laser beam direction (R) of the impulse and the surface to be formed. The redirecting arrangement is controlled so that the laser beam impulses impact at adjacent impact locations and form a pulse zone. With a positioning arrangement a relative movement between the pulse zone and the unfinished object of predetermined speed is established so that the pulse zone formed by the impact locations moves along the surface of the unfinished object and an ablation layer of a layer thickness (dS) is removed with each contour pass.