The configuration interaction, applied very recently byAsaad to the calculations ofKLL-Auger spectra, could remove the large discrepancies which existed for lowZ between experimental and theoretical relative group intensities I(KL1L2,3)/I(KL1L1) and I(KL2,3L2,3)/I(KL1L1).Asaad's calculations, however, were based on binding energies E(L1) and energies of the Coulomb and spin-orbit interaction, which were not very accurate. In the present calculations use has been made of more accurate binding energies E(L1) and Coulomb and spin-orbit interaction energies. It is shown that the absolute error in the results of the new calculations is less than 10%. From this it follows that the remaining discrepancies between theoretical and experimental values of the group intensities for 10≦Z<25 may be solely attributed to the inadequacy of the calculated transition probabilities. This calls for calculations of transition amplitudes of the KLL-process with more accurate wave functions for Z<25, in particular for Z=10.