Abstract: A partially hydrogenated fatty substance produced by partial hydrogenation of a substrate, such as vegetable, animal or marine oil, said partially hydrogenated substance having a low content of trans fatty acids. When the hydrogenation degree is below 30% the trans-fatty acid concentration can be expressed in the following way: trans≦0.3×(initial IV—IV) in %. of the total amount of fatty acids, wherein IV refers to iodine value. When the hydrogenation degree is between 30 and 70% the trans-fatty acid concentration can be expressed with: trans≦0.09×initial IV in % of the total amount of fatty acids. The partial hydrogenation is performed by a process in which the substrate, hydrogen gas and a solvent are mixed, and the whole mixture is brought into a supercritical or near-critical state. This substantially homogeneous super-critical or near-critical solution is led over the catalyst, whereby the reaction products formed, i.e.