Hydrodesulphurization of a gasoline cut containing hydrocarbons containing at least 2 carbon atoms per molecule and having an end point of 250° C. or less, by contacting the gasoline cut with at least one catalyst having an active phase of at least one metal from group VIII and at least one metal from group VIB deposited on a support, said catalyst being prepared using a process of: i) contacting support with precursors of group VIII and group VIB metals; ii) contacting support with at least one organic compound formed from at least one cyclic oligosaccharide composed of at least 6 α-(1,4)-bonded glucopyranose subunits; iii) drying to obtain at least said metal from group VIII and at least said metal from group VIB in the oxide form; then iv) sulphurization such that said active phase is in the sulphide form; i) and ii) being carried out separately, in any order, or simultaneously.