TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The method is carried out in two steps, the steps of hydrotreating and hydroisomerization are carried out in two separate reactors and the hydrotreating step is carried out in the presence of a catalyst comprising a mesostructured matrix containing silicon oxide and the hydroisomerization step is carried out in the presence of a catalyst comprising a mesostructured matrix comprising a mixture of silicon oxide and aluminum oxide. The method is carried out in a single step, the step of hydrotreating and hydroisomerization are carried out in a single reactor and hydroisomerization and hydrotreating steps are carried out in the presence of a single catalyst comprising a mesostructured matrix consisting of silicon oxide. Preferred Components: The polyoxometalates are tungsten compound of formula (H2W12O406-), phosphorus-molybdenum compound of formula (PMo12O403-) or phosphorus-tungsten compound of formula (PW12O403-) (both preferred), (PW12O403-), phosphorus-nickel compound of formula (HPNiMo11O406-), (P2Mo5O236-), nickel-molybdenum compound of formula (NiMo6O24H64-) and/or (Ni2Mo10O38H48-). The polyoxometalates are Keggin heteropolyanions of formula (XM12O40(q-)), where the ratio of m/x is 12 and lacunary Keggin heteropolyanions of formula (XM11O39(q-)), where the ratio of m/x is 11. The catalyst in the form of oxide has a non-spherical shape of each of the elementary particles. The catalyst comprises group VIB element (2-35 wt.%), group VIII element (0.1-10 wt.%), and doping element (0.1-10 wt.%) comprising phosphorus, boron or silicon.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The feedstock is oils and fats of vegetable or animal origin, or mixtures of such feedstock, containing triglycerides, free fatty acids and/or esters, crude or refined vegetable oils, in all or part, and derived from vegetable comprising rapeseed, sunflower, soybean, palm, palm kennel oil, olive, coconut and/or Jatropha. Preferred Definitions:    h = 0-6;    x = 0-2;    m = 5, 6, 7, 9, 10, 11 or 12;    y = 17 or 18; and    q = 3 or 12.