The sulfur electronic structure allows for the existence of hypervalent molecules that were discussed as early as 1939 by Schomaker and Pauling. In the present paper, we report a theoretical study of three hypothetical possible six-membered rings that contain the –N=S–S=N– motif carried out at the MP2/aug-cc-pVDZ level. Three minima have been found, of which two of them are six-membered rings with all covalent bonds. Since they do not have a planar structure, we have calculated the aromaticity index NICS through the symmetry axis perpendicular to the mid-plane and at various points in space. Benzene, cyclohexane, and 1,2,5-thiadiazole have served as points of comparison.