The potential function of the electronic ground state of the hydrogen sulphide molecule is obtained by the simultaneous fit of a very large sample of high-resolution vibration-rotation data. The use of an extensive set of more than 12000 experimental rovibrational transitions, corresponding to 4175 rovibrational states with J(max) = 15, K-a max = 15 for bands of 7 isotopomers ((H2S)-S-32, (H2S)-S-33, (H2S)-S-34, (D2S)-S-32, (D2S)-S-34, (HDS)-S-32, and (HDS)-S-34), allows improved calculations of 'local-mode states' and highly excited bending-rotational states. The root-mean-square (PMS) deviation of the rovibrational fit is 0.05 cm(-1). For the entire set of all 73 band centres of all isotopic species for which experimental data exists, the RMS deviation of the results of calculations with a single isotopic invariant potential function is 0.03 cm(-1).