The description refers to a process for the remelting of surfaces of workpieces with laser radiation, in particular of precoated surfaces. The invention is characterized by the fact that processing takes place with a laser beam which impinges on the workpiece surface at an angle of incidence deviating from zero in the processing direction, so that the remelting process takes place in a pricking process. It is of great advantage if the laser radiation is provided with linear polarization (p-polarized) and the absorption degree is adjusted by selecting an inclined angle of incidence corresponding to the Fresnel reflection curves.