The vertical electron detachment energies of Mg₂Cl₅^– and Mg₃Cl₇^– superhalogen anions were calculated at the outer valence Green function level with 6–311+G(3df) basis sets. These species were found to form rather unusual geometrical structures, each of which corresponds to a stable anionic state exhibiting superhalogen nature. The global minimum structure of Mg₂Cl₅^– was found to possess D_3h symmetry, which can be described as a system in which two central magnesium atoms are linked via a symmetrical triangle formed by three chlorine atoms, whereas the lowest-energy structure for Mg₃Cl₇^– was found to have C_3v symmetry, which can be viewed as a fragment of chloromagnesite crystal lattice. Extremely large electron binding energies of these anions (exceeding 6.5 eV in all cases) were predicted and discussed.