The structure and thermodynamic stability of methylnitrite and its anion are studied by the infinite-order coupled-cluster method with all singles and doubles and noniterative inclusion of triple excitations [CCSD(T)] and Hartree-Fock-density-functional theory (HFDFT). We have optimized the geometries and computed the harmonic vibrational frequencies of major fragments, H-2, CH, NH, OH, CN, N-2, CO, NO, O-2, CH2, NH2, H2O, HCN, HNC, HCO, HNO, O2H, CO2, NO2, CH3, NH3, CNH2, HCO2, HNO2, CH3N, CH3O, CH3NO, CH3ON, CH2NO2, and their anions, when the latter exist. Fragmentation energies obtained at both levels of theory are rather close to each other, except for channels involving CN as a product. The CH3ONO- and CH3NO2-anions are shown to possess lower fragmentation energies than their neutral parents. This implies that the attachment of an extra electron to CH3NO2 or CH3ONO may have a crucial role in initiating the decomposition of these compounds. Also, the attachment of an extra electron to CH3NO2 or CH3ONO leads to the appearance of new exothermic decay channels of the anions.