This is the second paper in a series of investigations on spin-orbit coupling (SOC) effects in dihydrides of third-row transition elements. The dissociation path of rhenium dihydride was explored using the multiconfiguration self-consistent-field method followed by diagonalization of SOC matrices, in which the Stevens-Basch-Krauss-Jasien-Cundari (SBKJC) basis sets were employed after adding one set of polarization functions for each atom. The most stable rhenium dihydride has a linear structure and its ground state is (6)Sigma(g)(+). Both C(2v) and C(s) dissociation paths into a Re atom and a hydrogen molecule (Re((6)S) + H(2)((1)Sigma(g)(+))) were explored on the potential energy curves of low-lying states. A relatively high energy barrier was obtained along the C(2v) path and two conical intersections were found at the H-Re-H angles of 29.8 degrees and 96.1 degrees along the C(2v) path. Since it was revealed that the geometrical deformation to C(s) symmetry at the H-Re-H angle of 29.8 degrees does not provide explicit lowering of the energy barrier for the dissociation, even after considering nonadiabatic couplings (NACs) in the neighborhood of the conical intersections, it can be concluded that the most feasible path is hopping from the lowest (6)A(1) state to the lowest (6)B(2) state at the H-Re-H angle of 96.1 degrees followed by hopping from the lowest (6)B(2) state back to the lowest (6)A(1) state at the H-Re-H angle of 29.8 degrees, where the latter crossing point is the highest in energy along this path. Thus, when the molecular system can reach the areas of these crossing points, the molecular system hops from one of the states to another owing to NAC or SOC effects; especially, SOC effects become important at the crossing point with C(2v) symmetry.