A process for the production of a high octane number gasoline cut starting from a light naphtha feed, comprising the following series of steps: a) a first step for separation by distillation carried out in a deisopentanizer, which can be used to separate hydrocarbons containing 5 carbon atoms from heavier compounds (i.e. iC5 or iC5+nC5, depending on the case), b) a section for catalytic isomerization of the heavy effluents obtained from the first separation step, followed by a stabilization of the isomerized effluent, which consists of separating out the compounds which are lighter than the pentanes, c) a second step for separation by distillation of the effluents from the isomerization reaction section, carried out using a deisohexanizer consisting of a separation column in which the overhead products and the bottom products are the desired products from the process, and in which an intermediate cut which is enriched in n-hexane, removed as a side stream, is recycled to the catalytic isomerization section, d) a step for transferring heat between the two separation steps, namely the condenser of the deisohexanizer and the reboiler of the deisopentanizer, carried out using an exchanger in order to condense all or a portion of the overhead vapours from the deisohexanizer by reboiling all or a portion of the bottom of the deisopentanizer column and using for this purpose a means which depends on the operating pressure of the deisohexanizer, process wherein transferring heat of step d) is performed according to two modes: - either by increasing the operating pressure of the deisohexanizer, which has the consequence of having to install a lateral reboiler which supplies the majority of the heat at a temperature which is substantially close to that of the bottom reboiler for said column when its operating pressure is selected so as to be the lowest possible permitted by the available cold utilities, - or by maintaining the operating pressure of the deisohexanizer at a level which is the lowest permitted by the available cold utilities, or even below this level, which causes the overhead vapours from the deisohexanizer to be compressed in a compressor in a manner such as to instigate the pressure and temperature conditions in the exchanger which can be used to provide the thermal requirements for the reboiler of the deisopentanizer with good efficiency. a) a first step for separation by distillation carried out in a deisopentanizer, which can be used to separate hydrocarbons containing 5 carbon atoms from heavier compounds (i.e. iC5 or iC5+nC5, depending on the case), b) a section for catalytic isomerization of the heavy effluents obtained from the first separation step, followed by a stabilization of the isomerized effluent, which consists of separating out the compounds which are lighter than the pentanes, c) a second step for separation by distillation of the effluents from the isomerization reaction section, carried out using a deisohexanizer consisting of a separation column in which the overhead products and the bottom products are the desired products from the process, and in which an intermediate cut which is enriched in n-hexane, removed as a side stream, is recycled to the catalytic isomerization section, d) a step for transferring heat between the two separation steps, namely the condenser of the deisohexanizer and the reboiler of the deisopentanizer, carried out using an exchanger in order to condense all or a portion of the overhead vapours from the deisohexanizer by reboiling all or a portion of the bottom of the deisopentanizer column and using for this purpose a means which depends on the operating pressure of the deisohexanizer, process wherein transferring heat of step d) is performed according to two modes: - either by increasing the operating pressure of the deisohexanizer, which has the consequence of having to install a lateral reboiler which supplies the majority of the heat at a temperature which is substantially close to that of the bottom reboiler for said column when its operating pressure is selected so as to be the lowest possible permitted by the available cold utilities, - or by maintaining the operating pressure of the deisohexanizer at a level which is the lowest permitted by the available cold utilities, or even below this level, which causes the overhead vapours from the deisohexanizer to be compressed in a compressor in a manner such as to instigate the pressure and temperature conditions in the exchanger which can be used to provide the thermal requirements for the reboiler of the deisopentanizer with good efficiency. - either by increasing the operating pressure of the deisohexanizer, which has the consequence of having to install a lateral reboiler which supplies the majority of the heat at a temperature which is substantially close to that of the bottom reboiler for said column when its operating pressure is selected so as to be the lowest possible permitted by the available cold utilities, - or by maintaining the operating pressure of the deisohexanizer at a level which is the lowest permitted by the available cold utilities, or even below this level, which causes the overhead vapours from the deisohexanizer to be compressed in a compressor in a manner such as to instigate the pressure and temperature conditions in the exchanger which can be used to provide the thermal requirements for the reboiler of the deisopentanizer with good efficiency.