A process for the desulphurization of a gasoline cut containing sulphur-containing compounds, olefins and diolefins, involving (a) fractionating the gasoline in order to recover a light gasoline cut LCN and a first heavy gasoline cut HCN; (b) desulphurization of the first heavy gasoline cut HCN; (c) partially condensing desulphurization effluent obtained from b) in a manner such as to produce a gaseous phase of hydrogen and H2S and a liquid hydrocarbon phase HCN of dissolved H2S; (d) separating the liquid hydrocarbon phase HCN into an intermediate gasoline cut MCN and a second heavy gasoline cut HHCN; (e) carrying out a second desulphurization of the second heavy gasoline cut HHCN.