The Ta bulk N 7 -level of TaC(111) decays either by the on-site Auger decay or by the interatomic off-site one. By the interatomic off-site Auger decay the subsurface core-hole is filled by a subsurface valence electron, and the excess energy is dissipated by the excitation of the neighboring surface N 7 electron to an unoccupied state, just above the Fermi level. The interatomic Auger decay is followed by the surface on-site Auger decay [R.A. Bartynski, S. Yang, S.L. Hulbert, C.-C. Kao, M. Weinert, D.M. Zehner, Phys. Rev. Lett. 68 (1992) 2247]. We showed by a many-body theory that the Ta N 7 -VV Auger-electron spectroscopy (AES) spectrum of TaC(111) produced by the surface Auger decay via the interatomic Auger decay, measured in coincidence with the bulk core-level photoemission coincides in both line shape and peak kinetic energy (KE) with the singles (noncoincidence) Ta N 7 -VV AES one produced by the surface Auger decay. This explains why Bartynski et al. [Phys. Rev. Lett. 68 (1992) 2247] could describe the coincidence Ta N 7 -VV AES spectrum of TaC(111) produced by the surface Auger decay via the interatomic Auger decay by a self-convolution of the valence band density of states (SCDOS) from the first atomic layer.