THE PRESENT INVENTION DISCLOSES A METHOD FOR PRODUCING FATS AND OILS RICH IN A X2U TRIGLYCERIDE, WHICH COMPRISES THE STEP OF FRACTIONATING FATS AND OILS WHICH COMPRISE 20 TO 60 MASS % OF A DI-SATURATED MONO-UNSATURATED TRIGLYCERIDE (X2U TRIGLYCERIDE) CONSISTING OF TWO SATURATED FATTY ACID RESIDUES AND ONE UNSATURATED FATTY ACID RESIDUE IN TOTAL TRIGLYCERIDES IN THE PRESENCE OF 1 TO 50 MASS % OF A FATTY ACID LOWER ALKYL ESTER COMPRISING 10 TO 100 MASS % OF AN UNSATURATED FATTY ACID LOWER ALKYL ESTER. THIS METHOD IS A MORE EFFICIENT AND INDUSTRIALLY SUITABLE FRACTIONATION AND PRODUCTION METHOD OF FATS AND OILS RICH IN A DI-SATURATED MONO-UNSATURATED TRIGLYCERIDE (X2U TRIGLYCERIDE).