An accurate single-valued double many-body expansion (DMBE) potential energy surface is reported for the ground electronic state of HSO based on novel MR CISD ab initio energies suitably corrected for the complete one-electron basis set/complete CI limit. To improve the accuracy of the fit, we have suggested a n-body distributed polynomial approach which implies using individual multinomial developments at the various stationary points. For simplicity, only the three most relevant such points have been considered: two minima (HSO, HOS) and the saddle point connecting them.