Spontaneous deamidation in the Asn-Gly-Arg (NGR) motif that yields an Asp-Gly-Arg (DGR) sequence has recently attracted considerable attention because of the possibility of application to dual tumor targeting. It is well known that Asn deamidation reactions in peptide chains occur via the five-membered ring succinimide intermediate. Recently, we computationally showed by the B3LYP density functional theory method, that inorganic phosphate and the Arg side chain can catalyze the NGR deamidation using a cyclic peptide, c[CH₂CO⁻NGRC]⁻NH₂. In this previous study, the tetrahedral intermediate of the succinimide formation was assumed to be readily protonated at the nitrogen originating from the Asn side chain by the solvent water before the release of an NH₃ molecule. In the present study, we found a new mechanism for the decomposition of the tetrahedral intermediate that does not require the protonation by an external proton source. The computational method is the same as in the previous study. In the new mechanism, the release of an NH₃ molecule occurs after a proton exchange between the peptide and the phosphate and conformational changes. The rate-determining step of the overall reaction course is the previously reported first step, i.e., the cyclization to form the tetrahedral intermediate.