TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: In the method (M1), stage (a) operates in presence of hydrogen mixed with the feedstock such that the hydrogen/feedstock ratio is 150-700 (preferably 150-650, especially 150-600 Nm3 hydrogen/m3 feedstock. The total proportion of oxides of group VIB and VIII metals in the catalyst used in stage (a) is 5-40 wt.% in relation to the total mass of catalyst. The mono-dimensional 10 MR zeolite molecular sieve is ZBM-30 synthesized with the triethylene tetramine organic structurant. The fixed bed hydroisomerization catalyst in stage (c) comprises a noble metal of 0.01-5 wt.% in relation to the finished catalyst. The method involves the group VIB metal the fixed bed hydroisomerization catalyst in stage (c) in content of 5-40 wt.%, in oxide equivalent, and the group VIII metal content the catalyst ranges of 0.5-10 wt.%, in oxide equivalent. The method (M2) further involves separating from the hydrotreatment effluent, hydrogen, other gases and at least one hydrocarbon-containing base, the separating being conducted prior to the hydroisomerization stage; and separating resultant effluent to recover at least one diesel fuel base. Preferred Components: The mono-dimensional 10 MR zeolite molecular sieve (S1) of the fixed bed hydroisomerization catalyst is selected from among the zeolite molecular sieves of TON structural type, including NU-10, EUO, selected from among EU-1 and/or ZSM-50, or zeolite molecular sieves ZSM-48, ZBM-30, IZM-1, COK-7, EU-2 and/or EU-11 (preferably ZSM-48, ZBM-30, IZM-1 and/or COK-7, especially ZSM-48 and/or ZBM-30, particularly ZBM-30). The hydroisomerization catalyst comprises either at least one noble metal of group VIII or at least one metal of group VIB, in combination with at least one non-noble metal of group VIII. The feedstock comprises at least one vegetable oil or animal fat (preferably palm, palm-nut, copra, castor and cotton oil, peanut, linseed, crambe and jatropha oil, an oil resulting from sunflower or rapeseed through genetic modification or hybridization, algae oil, waste kitchen oil and animal oil), essentially containing triglycerides and fatty acids or esters, with hydrocarbon fatty chains having number of carbon atoms of 6-25. EXAMPLE - No suitable example is given.