A fin MOS transistor is made from an SOI-type structure that includes a semiconductor layer on a silicon oxide layer coating a semiconductor support. A trench formed from the surface of the semiconductor layer delimits at least one fin in the semiconductor layer, that trench extending at least to an upper surface of the semiconductor support. Etched recesses in sides of a portion of the silicon oxide layer located under the fin are filled with a material selectively etchable over silicon oxide.