NOVELTY - Treating feedstocks obtained from a renewable source, comprises (a) hydrotreating of the feedstock in the presence of a fixed-bed catalyst, (b) separating, starting from the effluent i.e. obtained from stage (a), of hydrogen, gases, and at least one hydrocarbon base, (c) hydroisomerizing at least a portion of the hydrocarbon base i.e. obtained from stage (b) in the presence of a fixed-bed hydroisomerization catalyst, and (d) separating, starting from the effluent i.e. obtained from stage (c), of hydrogen, gases, and at least one gas oil base and one kerosene base.    USE - The process is useful for treating feedstocks obtained from a renewable sources, including the oils and fats of plant or animal origin, or mixtures of such feedstocks, containing triglycerides and/or free fatty acids and/or esters and the vegetable oils that can be raw or refined, totally or partially, and obtained from the following plants canola, sunflower, soybean, palm, palm-kernel, olive, coconut and Jatropha, and the animal fats including lard or fats composed of waste from the food industry or obtained from catering industries (all claimed).    ADVANTAGE - The process operates in a cost-effective and environmentally-friendly manner.    DETAILED DESCRIPTION - Treating feedstocks obtained from a renewable source, comprises (a) hydrotreating of the feedstock in the presence of a fixed-bed catalyst that comprises a hydro-dehydrogenating function comprising at least one metal of group VIII and/or group VIB, taken by itself or in a mixture, and a substrate i.e. formed by alumina, silica, silica-alumina, magnesia and/or clays, where the hydrotreatment stage operates at a temperature of 200-450 degrees C, at a pressure of 1-10 MPa, at an hourly volumetric flow rate of 0.1-10 hours-1, and in the presence of a total quantity of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio is 70-1000 Nm3 of hydrogen/m3 of feedstock, (b) separating, starting from the effluent i.e. obtained from stage (a), of hydrogen, gases, and at least one hydrocarbon base, (c) hydroisomerizing at least a portion of the hydrocarbon base i.e. obtained from stage (b) in the presence of a fixed-bed hydroisomerization catalyst, where the catalyst comprises at least one hydro-dehydrogenating metal i.e. formed by the metals of group VIB and group VIII of the periodic table and a substrate that comprises a zeolite that comprises at least one series of channels whose opening is defined by a ring with 8 oxygen atoms, modified by (a1) at least one stage for introducing at least one alkaline cation that belongs to group IA or IIA of the periodic table, (b1) a stage for treatment of the zeolite in the presence of at least one molecular compound that contains at least one silicon atom, (c1) at least one stage for partial exchange of the alkaline cations by ammonium (NH4+) cations, and (d1) at least one heat treatment stage, the hydroisomerization stage is carried out at a temperature of 150-500 degrees C, at a pressure of 1-10 MPa, at an hourly volumetric flow rate of 0.1-10 hours-1, and in the presence of a total quantity of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio is 70-1000 Nm3/m3 of feedstock, and (d) separating, starting from the effluent i.e. obtained from stage (c), of hydrogen, gases, and at least one gas oil base and one kerosene base.