The equilibrium geometries, total energies, and vibrational frequencies of anions X(2)Y(2)(-) (X = C, Si, Ge and Y = N, P, As) are theoretically investigated with density functional theory (DFT) method. Our calculation shows that for C(2)N(2)(-) species, the D(2h) isomer is the most stable four-membered structure, and for other species the C(2v) isomer in which two X atoms are contrapuntal is the most stable structure at the B3LYP/6-311 +G(*) level. Wiberg bond index (WBI) and negative nucleus-independent chemical shift (NICS) value indicate the existence of delocalization in stable X(2)Y(2)(-) structures. A detailed molecular orbital (MO) analysis further reveals that stable isomers of these species have strongly aromatic character, which strengthens the structural stability and makes them closely connected with the concept of aromaticity.