The present invention relates to a process for making a fatty preparation to be incorporated in a meat or cheese product or in a product for feeding animals, wherein said fatty preparation does not comprise fats with a plant origin saturated fat content higher than 25% by weight nor fats with an animal origin saturated fat content higher than 15% by weight nor trans fats. The present invention further relates to a fatty preparation and to a meat or cheese product or product for feeding animals comprising the same.