The reaction pathway of the formation of 3,4-dinitrofuroxan from glyoxime is theoretically investigated under experimental conditions with 25 % nitric acid and dinitrogentetroxide reagents to clarify the mechanism of formation of a furoxan ring by glyoxime. The geometric configurations of minima and transition-state species are optimized at the (U)B3LYP/6-311++G** level. The CCSD(T) and CASSCF(10e,8o)/CASSCF(9e,8o) single-point energy corrections at the same level are performed on top of the optimized geometries. A subsequent dynamic correlation by using NEVPT2/6-311++G**-level single-point energy calculations based on the CASSCF results is also performed to obtain accurate energy values. The formation reaction is analyzed from two processes: glyoxime nitration and 3,4-dinitroglyoxime (nitration product) oxidative cyclization. Calculation results indicate that the electrophilic substitution of nitronium ions from the protonated HNO3 and the abstraction of hydrogen ions by HNO3 molecules are requisites of glyoxime nitration. The formation of a furoxan ring from 3,4-dinitroglyoxime involves two possible mechanisms: 1) oxydehydrogenation by NO2 molecules and the subsequent torsion of NO radical groups to form a ring and 2) the alternation of dehydrogenation and cyclization. The intermediates and transition states in both routes exhibit monoradical and diradical characteristics. Singlet and triplet reactions are considered for the diradical species. Results show that the singlet reaction mechanism is more favorable for cyclization than the triplet reaction. The formation of a furoxan ring from oxime is in accordance with the stepwise intermolecular dehydrogenation and intramolecular torsion to the ring.