The maximum coordination number of the central atom in planar molecules generated by now in mole-cular beams was 8. We made use of the chemical bond model developed for planar boron clusters to check the possibility of existence of planar molecules with the coordination numbers 9 and 10. The objects of or study were the AlB₉ and AlB₁₀⁺ clusters which have local minima corresponding to highly symmetrical D _9h and D _10h structures, respectively. According to our calculations, the highly symmetrical structure of AlB₉ is a global minimum or a low-lying isomer, and, therefore, it holds promise as a new ligand for coordination chemistry. The energy of the highly symmetrical structure of AlB₁₀⁺ with the coordination number 10 is too high, and this structure is hardly synthetically feasible. Thus, 9 is presently the maximum coordination number of an atom in a planar molecule.