The present invention describes a process for the isomerization of paraffinic feedstocks operating at a temperature of between 200° C. and 500° C., at a total pressure of between 0.45 MPa and 7 MPa, at a hydrogen partial pressure of between 0.3 and 5.5 MPa, at an hourly space velocity of between 0.1 and 10 kilograms of feedstock introduced per kilogram of catalyst and per hour and using a catalyst comprising at least one metal of group VIII of the periodic table of elements, at least one matrix and at least one zeolite IZM-2, in which the ratio between the number of moles of silicon and the number of moles of aluminium of the zeolite IZM-2 network is between 25 and 55, preferably between 25 and 50, and preferably between 30 and 50.