ABSTRACT Despite hydrogen sulphide (H2S) has been predicted to be the major reservoir of S-bearing species on the icy mantles of interstellar grains, no solid H2S has been detected so far. A crucial parameter that governs whether or not a species remains frozen on to the grain mantles is its binding energy (BE). We present a new computational study of the H2S BE on a large amorphous water ice surface, constituted by 200 water molecules. The resulting H2S BE distribution ranges from 57 K (0.5 kJ mol−1) to 2406 K (20.0 kJ mol−1), with the average μ = 984 K (8.2 kJ mol−1). We discuss the reasons why the low bound of the newly computed BE distribution, which testifies to the very weak interaction of H2S with the ice surface, has never been found by previous theoretical or experimental works before. In addition, the low H2S BEs may also explain why frozen H2S is not detected in interstellar ices. Following previous molecular dynamics studies that show that the energy of reactions occurring on ice surfaces is quickly absorbed by the water molecules of the ice and conservatively assuming that 10 per cent of the HS + H → H2S formation energy (−369.5 kJ mol−1) is left to the newly formed H2S, its energy is more than twice the largest BE and five times the average BE and, hence, H2S will most likely leave the water surface.