A process for the isomerization of a feed of hydrocarbon compounds containing C5 and/or C hydrocarbon compounds, comprising: a) supplying an isomerization unit with at least one liquid fraction of the feed of hydrocarbon compounds and isomerizing the feed in the presence of a chlorinated catalyst; b) supplying a stabilization unit containing at least one stabilization column with the effluent obtained from the isomerization unit and separating the effluent; c) providing an absorption unit having one absorption column; d) extracting a liquid flow enriched in chlorinated compounds from the absorption unit which is recycled to the isomerization unit; and e) extracting the liquid flow containing at least one isomerate from the stabilization unit.