New quantum dynamics computations of the rate constant for the atmospheric reaction H + O-3 --> O-2 + OH are reported. These calculations have been carried out under the assumption of an atom-to-atom reactive process scheme rather than on the basis of the global atom-molecule reactive scattering approach reported in a previous paper by the same authors (J. Phys. Chem. 1997, 101, 8817). Agreement with the available classical trajectory results are now notably improved, although the new theoretical results still continue to agree best with the more recent experimental data of Clyne and Monkhouse and Greenblatt and Wiesenfeld for the title reaction.