For conversion of sulphur-containing compounds present in a gas comprising H2S and sulphur-containing compounds into additional H2S, a step A of contacting the gas with a reducing gas and a hydrogenation catalyst comprising cobalt, molybdenum and an alumina support, the sum of cobalt and molybdenum, in the oxide form, being 3% to 25% by weight, the surface area of alumina being more than 140 m2/g. In step B, effluent gas from step A is contacted with a catalyst comprising at least one alkaline-earth element, at least one dopant being iron, cobalt or molybdenum and at least one compound of titanium oxide and/or zirconium oxide, the catalyst for step B) being either in bulk or supported.