A process for the isomerization of a feed of hydrocarbon compounds comprising C 5 and/or C 6 hydrocarbon compounds, said process comprising a loop for recycling at least one chlorinated compound, and in which process: a) an isomerization unit is supplied with at least one liquid fraction of said feed of hydrocarbon compounds and the isomerization is carried out in the presence of a chlorinated catalyst; b) a stabilization unit comprising at least one stabilization column is supplied with the effluent obtained from the isomerization unit and a separation is carried out in said stabilization unit into: • a gaseous effluent comprising at least one chlorinated compound; • a liquid effluent comprising a concentration C A of C 5+ compounds; and • a liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds; c) the following is carried out in an absorption unit comprising only one absorption column: • a first contact between the gaseous effluent obtained from step b) and a washing fluid, said gaseous effluent being supplied to the absorption column below the supply for said washing fluid, said washing fluid being selected from a complementary liquid fraction of said feed of hydrocarbon compounds and/or at least a portion of said liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds obtained from step b); said washing fluid comprising a concentration C B of C 5+ compounds, with C A < C B; • a second contact between the gaseous flow resulting from said first contact and said liquid effluent obtained from step b), said liquid effluent being supplied to the head of the absorption column above said washing fluid; d) a liquid flow enriched in chlorinated compounds is extracted from the absorption unit and returned to the isomerization unit; e) said liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds is extracted from the stabilization unit. a) an isomerization unit is supplied with at least one liquid fraction of said feed of hydrocarbon compounds and the isomerization is carried out in the presence of a chlorinated catalyst; b) a stabilization unit comprising at least one stabilization column is supplied with the effluent obtained from the isomerization unit and a separation is carried out in said stabilization unit into: • a gaseous effluent comprising at least one chlorinated compound; • a liquid effluent comprising a concentration C A of C 5+ compounds; and • a liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds; • a gaseous effluent comprising at least one chlorinated compound; • a liquid effluent comprising a concentration C A of C 5+ compounds; and • a liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds; c) the following is carried out in an absorption unit comprising only one absorption column: • a first contact between the gaseous effluent obtained from step b) and a washing fluid, said gaseous effluent being supplied to the absorption column below the supply for said washing fluid, said washing fluid being selected from a complementary liquid fraction of said feed of hydrocarbon compounds and/or at least a portion of said liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds obtained from step b); said washing fluid comprising a concentration C B of C 5+ compounds, with C A < C B; • a second contact between the gaseous flow resulting from said first contact and said liquid effluent obtained from step b), said liquid effluent being supplied to the head of the absorption column above said washing fluid; • a first contact between the gaseous effluent obtained from step b) and a washing fluid, said gaseous effluent being supplied to the absorption column below the supply for said washing fluid, said washing fluid being selected from a complementary liquid fraction of said feed of hydrocarbon compounds and/or at least a portion of said liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds obtained from step b); said washing fluid comprising a concentration C B of C 5+ compounds, with C A < C B; • a second contact between the gaseous flow resulting from said first contact and said liquid effluent obtained from step b), said liquid effluent being supplied to the head of the absorption column above said washing fluid; d) a liquid flow enriched in chlorinated compounds is extracted from the absorption unit and returned to the isomerization unit; e) said liquid flow comprising at least one isomerate of the feed of hydrocarbon compounds is extracted from the stabilization unit.