NOVELTY - Treating feedstock from renewable vegetable/animal source involves (a) subjecting feedstock to hydrotreatment in presence of fixed-bed catalyst and hydrogen mixed with feedstock such that hydrogen/feedstock ratio is 150-750 Nm3 hydrogen/m3 feedstock, (b) separation of hydrogen, other gases and hydrocarbon-containing base, (c) hydroisomerization of base in presence of selective catalyst, the stage (c) is carried out in presence of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio is 70-1000 Nm3/m3 feedstock, (d) separation of diesel fuel base.    USE - For treating feedstock from renewable vegetable or animal source for preparing diesel fuel bases (claimed).    ADVANTAGE - The method allows, from feedstocks coming from renewable sources, to obtain high diesel fuel base yields while allowing reduced hydrogen consumption; maximizes the diesel fuel yield with excellent quality including low sulfur, nitrogen and aromatics content, an excellent cetane number due to the substantially paraffinic structure of the hydrocarbons formed, good cold strength properties due to the degree of isomerization of the paraffins of the cut, a low density (less than 800 kg/m3), which is an advantage insofar as the specification for the diesel fuel pool that is 845 kg/m3 maximum is more easily obtained.    DETAILED DESCRIPTION - Treating a feedstock from a renewable vegetable or animal source involves (a) subjecting the feedstock to hydrotreatment in presence of fixed-bed catalyst containing hydro-dehydrogenizing function and an amorphous support, at 200-450 degrees C., at a pressure of 1-10 MPa, at hourly space velocity of 0.1-10-1 and in presence of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio is 150 and 750 Nm3 hydrogen/m3 feedstock to produce an effluent, (b) separation, from the effluent from stage (a), of the hydrogen, other gases and at least one hydrocarbon-containing base, (c) hydroisomerization of at least part of the hydrocarbon-containing base from stage (b) in presence of fixed-bed hydroisomerization selective catalyst, the catalyst comprising at least one group VIII metal and/or at least one VIB group metal and at least one mono-dimensional 10 MR zeolite molecular sieve, the stage (c) is carried out at 150-500 degrees C, at pressure of 1-10 MPa, at an hourly space velocity of 0.1-10 h-1 and in presence of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio is 70-1000 Nm3/m3 feedstock to produce an effluent, (d) separation, from the effluent from stage (c), of the hydrogen, other gases and at least one diesel fuel base. An INDEPENDENT CLAIM is included for method (M2) involving providing an effluent from a hydrotreatment of a renewable animal or vegetable source and subjecting the effluent to a hydroisomerization stage with at least one hydroisomerization catalyst comprising at least one group VIII and/or group VI metal and at least one mono-dimensional 10 MR zeolite molecular sieve (S1).