Energies of the 15 lowest Rydberg states of the metastable H-4 cluster have been determined using Koopman's theorem at the equilibrium geometry of the par ent ion. H-4(+) To represent the core orbitals of H-4, a 6-31 G** basis set has been used at the SCF, MP2, MP4(SDTQ), CI-SD, and CI-SDT levels. The Rydberg orbitals have been modeled using a basis set analogous to that used to model the Rydberg orbitals of H-3 in previous theoretical calculations. To test the validity of the calculations for the H-4 molecule, ab initio calculations were repeated for the Rydberg orbitals of the H-3 molecule at the stable geometry of the H-3(+) core. Predicted transitions were within 2% of the rotational band spectra of H-3 observed by Herzberg. The metastable H-4 cluster formed from charge neutralization of H-4(+) decomposes into two H-2 molecules. Previous calculations have predicted that one of the two H-2 products will be vibrationally hot while the other will be relatively cold and that a large recoil energy of approximately 9 eV is expected for the relative kinetic energy of the two H-2 products. The present work suggests(2) that if Rydberg states are involved in the charge neutralization process, the recoil energy could be reduced due to radiative transitions among the Rydberg states.