Multiphoton decays of positronium

We compute the branching ratios for parapositronium and orthopositronium into four and five photons, respectively. We find GAMMA(p-Ps..-->..4..gamma..)/GAMMA(p-Ps..-->..2..gamma..) = 0.274(..cap alpha../..pi..)/sup 2/approx. = 1.48 x 10/sup -6/ and GAMMA(o-Ps..-->..5..gamma..)/GAMMA(o-Ps..-->..3..gamma..) = 0.177(..cap alpha../..pi..)/sup 2/approx. = 0.96 x 10/sup -6/. We also describe the energy spectra of photons from these decays.