Method for fabricating a strained semiconductor-on-insulator substrate, comprising: (a) the provision of a donor substrate comprising a monocrystalline semiconductor layer; (b) the provision of a receiving substrate comprising a surface layer of a strained monocrystalline semiconductor material; (c) the bonding of the donor substrate to the receiving substrate, a dielectric layer (13, 22) being at the interface between the surface layer and the monocrystalline silicon layer; (d) the transfer of the monocrystalline semiconductor layer from the donor substrate to the receiving substrate; (e) the cutting, by means of trench isolations extending into the receiving substrate beyond the strained semiconductor material layer, of a portion from a stack formed from the transferred monocrystalline semiconductor layer, from the dielectric layer and from the strained semiconductor material layer, said cutting operation resulting in the relaxation of the strain in the strained semiconductor material, and in the application of at least a part of said strain to the transferred monocrystalline semiconductor layer; wherein: - the donor substrate provided in step (a) comprises, in succession, a monocrystalline carrier substrate, an intermediate layer and said monocrystalline semiconductor layer, the intermediate layer forming an etch-stop layer with respect to the carrier substrate material and to the material of the monocrystalline semiconductor layer, step (d) comprising the transfer, to the receiving substrate, of the monocrystalline semiconductor layer, of the intermediate layer and of a portion of the carrier substrate; and - between steps (d) and (e), a first operation of selectively etching said portion of the carrier substrate with respect to said intermediate layer and a second operation of selectively etching said intermediate layer with respect to the monocrystalline semiconductor layer are implemented. (a) the provision of a donor substrate comprising a monocrystalline semiconductor layer; (b) the provision of a receiving substrate comprising a surface layer of a strained monocrystalline semiconductor material; (c) the bonding of the donor substrate to the receiving substrate, a dielectric layer (13, 22) being at the interface between the surface layer and the monocrystalline silicon layer; (d) the transfer of the monocrystalline semiconductor layer from the donor substrate to the receiving substrate; (e) the cutting, by means of trench isolations extending into the receiving substrate beyond the strained semiconductor material layer, of a portion from a stack formed from the transferred monocrystalline semiconductor layer, from the dielectric layer and from the strained semiconductor material layer, said cutting operation resulting in the relaxation of the strain in the strained semiconductor material, and in the application of at least a part of said strain to the transferred monocrystalline semiconductor layer; - the donor substrate provided in step (a) comprises, in succession, a monocrystalline carrier substrate, an intermediate layer and said monocrystalline semiconductor layer, the intermediate layer forming an etch-stop layer with respect to the carrier substrate material and to the material of the monocrystalline semiconductor layer, step (d) comprising the transfer, to the receiving substrate, of the monocrystalline semiconductor layer, of the intermediate layer and of a portion of the carrier substrate; and - between steps (d) and (e), a first operation of selectively etching said portion of the carrier substrate with respect to said intermediate layer and a second operation of selectively etching said intermediate layer with respect to the monocrystalline semiconductor layer are implemented.