Although an efficient DFT method using the generalized transition-state model to calculate core-electron binding energies had been successfully applied to over 200 cases, with an average absolute deviation of only 0.21 eV from experiment, a new DeltaE(KS)(PW86-PW91)/cc-pCVTZ model based on total Kohn-Sham energy difference was recently developed. Not only was the model error-free, but also the average absolute deviation for 32 cases studied was found to be 0.15 eV. In this study, we first confirm the excellent performance of such a DeltaE(KS) approach with 46 new cases, with the result that the average absolute deviation from experiment for the 78 cases remains at 0.15 eV. With such consistent accuracy, this new method is applied to the peptide bond. The model molecules studied in this work include formamide, N-methylformamide, N,N-dimethylformamide, acetamide, N-methylacetamide, N,N-dimethylacetamide, and two model dipeptides, one cyclic and one acyclic. The difference in the computed nitrogen core-electron binding energy between the two model dipeptides is found to be 0.85 eV, several times our average absolute deviation. This may be of interest to other workers studying other aspects of the peptide bond.