Supercell method is used to study the relaxation and screening effects during the Auger transition in metals. In order to make the interaction between the core-holes sited at different atoms negligible, the real metal is simulated by supercells repeated periodically. The electronic states concerned by the Auger transition are calculated by using FLAPW method. The occurrence of both bandlike and quasi-atomiclike Auger spectra across transition metal series is related clearly to the different responses of these metals to the existence of a core-hole depending on whether their d-bands are partially or completely filled. As examples, L_3VV and M_1VV Auger spectral profiles of Cu have been calculated in a reasonably well agreement with experiment. The hole-hole interaction is considered explicitly in the calculation to give the multi-splitting in the quasi-atomiclike Auger spectra.