Although many 1,2,3,4-tetrazine-1,3-dioxide derivates have been synthesized, [1,2,5] oxadiazolo [3,4-e] [1,2,3,4]-tetrazine-4,6-di-N-dioxide (FTDO) is the only one with high enthalpy of formation and high detonation velocity. Whereas, its stability has not been studied. In the present work, the structure of FTDO was investigated using density functional theory (DFT) method, and its stability was calculated by potential energy surface scanning and structure interconvert thermodynamics under different temperatures. The spontaneous isomerization of FTDO and its effect on the stability of FTDO were investigated. The dissociation of FTDO to N2, N2O and furoxan fragments was studied, and the possibility of synthetic route from FTDO to TTTO was discussed.