We report here a refinement of the potential energy surface for the electronic ground state of the H 2 32 S molecule in a least-squares fit to experimental spectroscopic data. The calculations are carried out by combining an exact kinetic energy (EKE) approach to the calculation of the rotation-vibration energies of a triatomic molecule with the MORBID approach, which employs an approximate kinetic energy operator. The combined method has been described and applied to the water molecule in two previous publications [O. L. Polyansky, P. Jensen, and J. Tennyson, J. Chem. Phys. 101, 7651-7657 (1994); ibid., submitted for publication.]. The input data for the fit of the present work comprised rotationvibration term values with J Β£ 10 for the vibrational ground state and the n 2 state, and with J Β£ 5 for all other states that have been characterized by high-resolution spectroscopy. In total, we fit data for 31 vibrational states of H 2 32 S. We have obtained a very accurate potential within the framework of the EKE approach. The root-mean-square deviation for the fitted vibrational energies was found to be 0.28 cm 01 . The fit to all 450 input data had a standard deviation of 0.17 cm 01 . In the final fit, 11 parameters were varied. Our analysis of the residuals (observed 0 calculated) from the fit provides even stronger evidence than analogous fits for water that we have reached a level of accuracy at which the breakdown of the Born-Oppenheimer approximation becomes the most important reason for the deviation between theory and experiment. In order to improve further the fit, the J, K a -dependent nonadiabatic corrections to the kinetic energy operator for the nuclear motion must be explicitly considered.