The present invention concerns a process for the desulphurization of a gasoline cut containing sulphur-containing compounds, olefins and diolefins, comprising at least the following steps: a) fractionating the gasoline in order to recover a light gasoline cut LCN and a first heavy gasoline cut HCN; b) carrying out a first step for desulphurization of the first heavy gasoline cut HCN; c) partially condensing the first desulphurization effluent obtained from step b) in a manner such as to produce a gaseous phase essentially constituted by hydrogen and H2S and a liquid hydrocarbon phase HCN comprising 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 step for desulphurization of the second heavy gasoline cut