We have studied the line shapes of Cu(001)-p (2 x 2)S L₂VV and L₃VV Auger decay by means of Auger photoelectron coincidence spectroscopy. Measuring the LVV Auger spectrum in coincidence with S 2p_1/2 and 2p_3/2 photoelectrons respectively, we have been able to separate the two overlapping Auger spectra and determine their intrinsic line shapes. The two Auger transitions, though shifted in energy, display an identical line shape whose main features can be qualitatively understood considering a single particle approximation but are better described within a Cini-Sawatzky (CS) approach. Comparison between the experimental and the CS calculated spectra confirms that a substantial part of the Auger lines ( ∼ 20%) can be ascribed to decay events accompanied by the excitation of one additional electron-hole pair in the valence band. For the first time, the locality of the Auger process combined with the surface sensitivity of the APECS technique and its ability to separate overlapping structures are used to study Auger transitions taking place at the the surface states of a S/noble-metal interface.