Starting from the CoXnH2O−DioxH2−L system, where DioxH2 = MH2 (methylglyoxime), DH2 (dimethylglyoxime) MEH2 (methylethylglyoxime), NioxH2 (1,2-cyclohexanedionedioxime), DfH2 (diphenylglyoxime), or FurH2 (furylglyoxime); L = Thio (thiocarbamide), Py (pyridine), An (aniline), NH3, PPh3 (triphenylphosphine), or SAM (sulfanilamide); X = F-, [BF4]-, [PF6]-, [SbF6]-, [BeF4]2-, [SiF6]2-, [TiF6]2-, [ZrF6]2-, [AlF6]3-, a series of coordinative compounds with the general formula of [Co(DioxH)2(L)2]XnH2O have been synthesized; their composition, structure, and some properties have been established. In addition, the substitution of some ligands from the axial position has been studied. The inclusion of fluoride anions in the studied dioximates creates favorable conditions for the formation of some complex hydrogen bond networks, which improves the crystallization process and increases the stability of the complexes. For the compounds containing both Co(III) and Rh(III) cations, it has been established that, according to Pearson, the Rh(III) cation prefers to form complex cations with thiocarbamide rather than with dioxime, while both DioxH- (DH- and NioxH-) and thiocarbamide coordinate to Co(III).