THE PRESENT INVENTION DISCLOSES A SAFER, MORE EFFECTIVE AND INDUSTRIALLY SUITABLE METHOD FOR PRODUCING FATS AND OILS RICH IN A XUX TRIGLYCERIDE WHEREIN THE CONTENTS OF A XXX TRIGLYCERIDE AND A XX DIGLYCERIDE ARE LOW WHICH COMPRISES, UPON REMOVING BY CRYSTALLIZATION A XXX TRGLYCERIDE AND A XX DIGLYCERIDE EACH OF WHICH IS CONTAINED IN FATS AND OILS COMPRISING 50 TO 90 MASS % OF A XUX TRIGLYCERIDE IN TOTAL TRIGLYCERIDES, THE STEP OF CONDUCTING SUCH REMOVING BY CRYSTALLIZATION IN THE PRESENCE OF A FATTY ACID LOWER ALKYL ESTER. THIS METHOD IS A MORE EFFICIENT AND INDUSTRIALLY SUITABLE METHOD FOR PRODUCING FATS AND OILS RICH IN A XUX TRIGLYCERIDE WHEREIN THE CONTENTS OF A XXX TRIGLYCERIDE AND A XX DIGLYCERIDE ARE LOW.