Abstract: A process for the treatment of an olefinic fraction, using a catalyst prepared by a process comprising: a) The preparation of a colloidal oxide suspension of a first metal M1 by the neutralization of a basic solution by an acidic mineral solution that contains the precursor of the metal M1, b) Bringing into contact the precursor of the promoter M2, either directly in its crystallized form or after dissolution in aqueous phase, with the colloidal suspension that is obtained in stage a), c) Bringing into contact the colloidal suspension that is obtained in stage b) with the substrate, d) Drying at a temperature of between 30° C. and 200° C., under a flow of air.