The potential energy surface (PES) for the loss of HCN or HNC from the pyrazine molecular ion was determined based on quantum chemical calculations using the G3//B3LYP method. Four possible dissociation pathways to form four $C_3H_3N^{+{{ullet}}$ isomers were examined. A Rice-Ramsperger-Kassel-Marcus quasi-equilibrium theory model calculation was performed to predict the dissociation rate constant and the product branching ratio on the basis of the obtained PES. The resultant rate constant for the HCN loss agreed with the previous experimental result. The kinetic analysis predicted that the formation of $CH=CHN{equiv}CH^{+{ullet}}+HCN$ was predominant, which occurred by three consecutive steps, a C-C bond cleavage to form a linear intermediate, a rearrangement to form an H-bridged intermediate, and elimination of HCN.