A method of manufacturing a composite structure comprises: a) providing a donor substrate of a single-crystal semiconductor material, b) implanting ions into the donor substrate, excluding an annular peripheral region, to form a buried brittle plane, the implantation conditions defining a first thermal budget for obtaining bubbling on a face of the donor substrate and a second thermal budget for obtaining a fracture in the brittle plane, c) forming a stiffening film on the donor substrate, carried out by applying a thermal budget lower than the first thermal budget, the stiffening film being perforated in the form of a mesh, the perforated stiffening film leaving a plurality of zones of the front face bare, d) depositing a carrier substrate on the donor substrate carried out by applying a thermal budget greater than the first thermal budget, and e) separating the donor substrate along the brittle plane.