A new, hitherto unknown bound state of the positronium molecule, with orbital
angular momentum L=1 and negative parity is reported. This state is stable
against autodissociation even if the masses of the positive and negative
charges are not equal. The existence of a similar state in two-dimension has
also been investigated. The fact that the biexcitons have a second bound state
may help the better understanding of their binding mechanism.Comment: Latex, 8 pages, 2 Postscript figure