The study on molecule m2N2 (m=H, Li, Na, Be, Mg, B, Al, C, Si, N, P, O, S, F, Cl) with symmetrical groups D~h and D2h had been conducted by using Ab Initio method. As a part of HyperChem pro 6.0, this program was operated with Pentium 4. The research involved a number of linear cyclic molecules m-N-N-m as well as m-N-m-N. As the result of the computation process, it was found that generally the cyclic molecules m2N2 were more stable than those of the other linear molecules signed with the smaller total energy. It was also found that the most stable linear molecules were NºN resulted from the optimalization of Cl-N-N-Cl with the total molecule energy: -637778.1251 kcal/mol. Meanwhile, the most stable cyclic molecules were S-N-S-N with the total molecule energy: -560789.9726 kcal/mol.