An accurate quantum investigation of vibrational relaxation induced by collision: para-H-2(v(1) = 1, j(1) = 0) +para-H-2(v(2) = 0, j(2) = 0) --> para-H-2(v'(1) = 0, j'(1)) + para-H-2(v'(2) = 0, j'(2)), is presented. The Hamiltonian within the coupled-states approximation is discretized in a mixed grid/basis representation and its action is computed in appropriate representations facilitated by a series of one-dimensional pseudo-spectral transformations. Furthermore, the parity and diatomic exchange symmetry are adapted to improve efficiency. S-matrix elements at numerous collision energies up to 2.2 eV are calculated from the Fourier transform of correlation functions obtained from the Chebyshev propagation. Partial wave contributions from J = 0 to 90 are obtained explicitly. Finally, thermal rate constants are computed over a wide range of temperatures (0-3500 K) and compared with available experimental measurements. In addition, the effect of initial rotational excitation on the relaxation probability is investigated. (C) 2003 Elsevier Science B.V. All rights reserved.