The relative spectral intensity of the band-like two M 4,5 -hole state to the atomic-like localized one is much suppressed in the coincidence M 3 –M 4,5 M 4,5 super Coster–Kronig (sCK) electron spectrum of Cu metal compared to the one in the coincidence L 3 –M 4,5 M 4,5 Auger electron spectroscopy (AES) spectrum. The M 3 -hole lifetime width of Cu metal is calculated by an ab initio atomic many-body theory (the extended relaxed core random phase approximation with exchange). The calculated M 3 -hole lifetime width of Cu metal agrees well with the experimental one. The M 3 –M 4,5 M 4,5 sCK decay width of Cu metal decreases much with delocalization of the two M 4,5 holes in the sCK final state, whereas the Auger decay width is fairly independent of localization and delocalization of the two M 4,5 holes in the Auger final state. Thus, the relative spectral intensity of the band-like state is much suppressed in the coincidence M 3 –M 4,5 M 4,5 sCK-electron spectrum of Cu metal compared to the one in the coincidence L 3 –M 4,5 M 4,5 AES spectrum.