The invention concerns a process for reducing the benzene content of petrol fractions and isomerizing paraffins in the presence of an isomerization catalyst comprising 4 to 15% of at least one halogen and at least one metal from group VIII deposited on a support composed of a mixture of specific proportions of eta alumina and gamma alumina, in which isomerization is carried out on a mixture of a) a feed with the following composition by weight: 40% to 80% of paraffins, 0.5% to 7% of cyclic hydrocarbons and 6% to 45% of aromatics, and with a maximum distillation temperature of between 70.degree. C. and 90.degree. C., b) a C.sub.5 -C.sub.6 cut which is generally a straight run cut, and c) a chlorine-containing compound providing a concentration of 50-5000 ppm of chlorine in the mixture.