A process for the isomerization of a light naphtha, said process comprising an isomerization reaction step, said step being carried out under the following conditions: - a temperature in the range 110°C to 240°C, - a pressure of 2 to 35 bar (1 bar = 0.1 MPa), and - a molar ratio of hydrogen/hydrocarbons in the range 0.1/1 to 1/1, - a space velocity of 1 to 4 h -1, the catalysts used being constituted by a support of high purity alumina preferably comprising 2% to 10% by weight of chlorine, 0.1% to 0.40% by weight of platinum, and optional other metals, said isomerization step being followed by a step for stabilization of the reaction effluents, and by two steps for separation by distillation of the bottom stream obtained from the stabilization step which are placed downstream of the stabilization step: 1- a first step for separation by distillation (block (3+4) in order to separate the hydrocarbons containing 5 carbon atoms from heavier compounds sent towards the second section for distillation by separation, said first separation step comprising two columns, a deisopentanizer and a depentanizer, disposed in series, i.e. the bottom stream from the deisopentanizer is supplied to the depentanizer, the stream of isopentane leaves from the head of the column, a stream enriched in hydrocarbons which are heavier than pentanes leaves from the bottom of the column and is supplied to the deisohexanizer, and the overhead stream from the column is recycled to the isomerization unit, and producing the following 3 cuts: a) a cut which is enriched in isopentane which is a product of the process, b) a cut which is enriched in n-pentane which is recycled to the reaction section, and c) a cut which is enriched in hydrocarbons which are heavier than pentanes, which is directed towards a second separation step, 2- a second separation step, consisting of a separation column wherein the overhead and bottom products are the products from the unit, namely an overhead stream which is rich in C6 branched compounds, a bottom stream, and an intermediate cut which is enriched in n-hexane, removed as a side stream which is recycled to the reaction section, in which isomerization process an exchange of heat is carried out: - between the condenser of the deisohexanizer and either the reboiler of the depentanizer or the reboiler of the deisopentanizer, or both, and - between the condenser of the depentanizer and the reboiler of the deisopentanizer. - a temperature in the range 110°C to 240°C, - a pressure of 2 to 35 bar (1 bar = 0.1 MPa), and - a molar ratio of hydrogen/hydrocarbons in the range 0.1/1 to 1/1, - a space velocity of 1 to 4 h -1, 1- a first step for separation by distillation (block (3+4) in order to separate the hydrocarbons containing 5 carbon atoms from heavier compounds sent towards the second section for distillation by separation, said first separation step comprising two columns, a deisopentanizer and a depentanizer, disposed in series, i.e. the bottom stream from the deisopentanizer is supplied to the depentanizer, the stream of isopentane leaves from the head of the column, a stream enriched in hydrocarbons which are heavier than pentanes leaves from the bottom of the column and is supplied to the deisohexanizer, and the overhead stream from the column is recycled to the isomerization unit, and producing the following 3 cuts: a) a cut which is enriched in isopentane which is a product of the process, b) a cut which is enriched in n-pentane which is recycled to the reaction section, and c) a cut which is enriched in hydrocarbons which are heavier than pentanes, which is directed towards a second separation step, 2- a second separation step, consisting of a separation column wherein the overhead and bottom products are the products from the unit, namely an overhead stream which is rich in C6 branched compounds, a bottom stream, and an intermediate cut which is enriched in n-hexane, removed as a side stream which is recycled to the reaction section, in which isomerization process an exchange of heat is carried out: - between the condenser of the deisohexanizer and either the reboiler of the depentanizer or the reboiler of the deisopentanizer, or both, and - between the condenser of the depentanizer and the reboiler of the deisopentanizer. - between the condenser of the deisohexanizer and either the reboiler of the depentanizer or the reboiler of the deisopentanizer, or both, and - between the condenser of the depentanizer and the reboiler of the deisopentanizer.