A fully relativistic discrete variational Xalpha calculation on OsO4 has been carried out. The ionization energies and orbital compositions are in good agreement with results from a variable photon energy photoelectron study. In particular, strong evidence is provided that the second and third bands in the photoelectron spectrum arise from the spin-orbit-coupled components of the lower ionization energy 2T2 primary ion state, derived from Os 5p and 6p atomic orbital contributions to the 3t2 molecular orbital.