TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The heterogeneous catalyst is selected from vanadyl phosphate dihydrate, supported TiO2, hydrotalcites, sulfuric acid, para-toluene-sulfonic acid and styrene-based sulfonic resins and mixed oxides of magnesium and aluminum.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The method involves the step of mixing the vegetable oils and/or animal fats with the aliphatic alcohol containing dialkyl carbonate, and obtaining a mix of vegetable oils and/or animal fats, aliphatic alcohols and dialkyl carbonate. The mix is placed in contact with the catalyst and is then heated. The mix is heated to a temperature of 50-200 degrees C (preferably 60-120 degrees C). The method is performed continuously or discontinuously (preferably in agitated or fixed-bed reactors). In the method, after the reaction, the heterogeneous catalysts are separated (preferably by filtration). After the reaction the aliphatic alcohols, if they have remained unreacted, are separated (preferably by distillation). After the reaction, a glycerin phase is separated (preferably by decantation). Preferred Components: The mix contains water and/or acids, before the reaction. The acid is present at a concentration of more than 1 wt.% expressed as oleic acid. The dialkyl carbonate is present in a quantity which is at least stoichiometric with respect to the water and the acid that are present in the mix. The aliphatic alcohol is 1-5C aliphatic alcohol (preferably methanol or ethanol). The aliphatic alcohol and the vegetable oil and/or animal fat are present in a weight ratio of 0.5 to 10. SPECIFIC COMPOUNDS - Dimethyl carbonate and diethyl carbonate are specified as the dialkyl carbonate.    EXAMPLE - A test was conducted with acid resin, dimethyl carbonate and methanol at 70 degrees C. An esterification test was conducted by using 18.8% oleic acid (OA) oil, an acid resin (15 wt.% with respect to the oil) and dimethyl carbonate (stoichiometric ratio equal to the ratio of the acid) and methanol as cosolvent (15 wt.% with respect to the weight of the oil). It was found that in 150 minutes of reaction the acidity dropped to 0.6%, giving a 96.8% conversion. A control test was conducted with acid resin and methanol at 70 degrees C. The control esterification test was conducted by using 25% OA acid oil, Resindion CFS/MB (RTM: dry polystyrene-based sulfonic acid exchange resin) (15 wt.% with respect to the oil) in the presence of methanol (15 wt.% with respect to the weight of the oil). The dry resin, dried in a stove at a temperature of 100 degrees C, and the methanol were added to the oil, which was initially homogenized and heated to a temperature of approximately 40 degrees C. The reaction occurred at the boiling point of methanol, 70 degrees C. The acidity dropped to 1.1% in 150 minutes, yielding 95.6% conversion. The results showed that the presence of dimethyl carbonate in the reaction system improved the performance of resin and allowed complete elimination of acidity.