Disclosed herein is a milk wherein the concentrations of palmitic acid and/or palmitoleic acid are higher than in traditional milk. At the same time the amounts of trans fatty acids and C6-C12 saturated fatty acids are lower than in traditional milk. In a preferred embodiment the milk has a fatty acid composition comprising at least 1.8% palmitoleic acid and/or at least 33% palmitic acid, and no more than 2% trans fatty acids. The invention also relates to food products which contain the milk according to the invention or part of it. The milk according to the invention has been produced by a process wherein to a lactating animal is given a feed which contains inside and on the surface of feed raw material particles a fatty acid mixture wherein the content of saturated fatty acids is over 90%.