Twelve stationary points have been characterized on the (H2S)2 potential energy surface using the MP2 and CCSD(T) methods with large, correlation consistent basis sets. To the best of our knowledge, five of the structures have not been identified elsewhere and are presented here for the first time. A similar analysis was performed on the ten, well-known structures of the water dimer in order to facilitate direct comparisons between the corresponding (H2O)2 and (H2S)2 configurations. Harmonic vibrational frequency computations identify three (H2S)2 configurations as minima, four as transition states, and five as higher-order saddle points (ni = 0, ni = 1, and ni ≥ 2, respectively, where ni is the number of imaginary frequencies). The two local minima and four transition state structures identified have electronic energies within 0.73 kJ mol-1 of the global minimum near the CCSD(T) complete basis set (CBS) limit, and the five higher-order saddle points range from 1.90 kJ mol-1 to 4.31 kJ mol-1 above the global minimum at the same level of theory. One of the more substantial differences observed between the H2S and H2O systems is that (H2O)2 has only a single minimum, while the other nine stationary points are significantly higher in energy ranging from 2.15 kJ mol-1 to 14.89 kJ mol-1 above the global minimum near the CCSD(T) CBS limit. For (H2S)2, the electronic dissociation energy of the global minimum is only 7.02 kJ mol-1 at the CCSD(T) CBS limit, approximately three times smaller than the dissociation energy of (H2O)2.