Disclosed is a method of making a natural, hard or semi-hard cheese product on the basis of a fat emulsion stabilized by a denatured, non-coagulated whey protein. This enables, inter alia, the production of cheese on the basis of fats having an increased content of unsaturated fatty acids. The method comprises coagulating a liquid that comprises milk protein and fat, said liquid comprising at least one oil-in-water emulsion, wherein said emulsion comprises the denatured, non-coagulated whey protein. Preferably the invention involves the use of at least two emulsions, the first being milk or cream, the second comprising a fat of increased content in unsaturated fatty acids, such as fractionated milk fat or vegetable fat.
