The invention relates to the production of a fatty product which has a low saturated fatty acid content and is free of trans-isomers, formulated from a fatty base containing mainly tripalmitin and/or fully hydrogenated palm oil.The fatty product of the invention fulfils nutritional and health requirements, has physical properties enabling the suitable use of same and meets organoleptic requirements of consumers.The fatty product can be used directly as an ingredient for the production of baked products, such as, cakes, biscuits and bread among others, and for the industrial and institutional deep frying of snacks, doughnuts, potatoes and other tubers and meats among other foods.