The invention relates to a method for transferring a useful layer (3) onto a support (4), comprising steps of forming a fragilisation plane (2) by implanting light species in a first substrate (1), so as to form a useful layer (3) between this plane and a surface of the first substrate (1); applying the support (4) onto the surface of the first substrate (1) in order to form an assembly (5) to be fractured; fragilisation heat treating the assembly (5) to be fractured; and initiating and propagating a fracture wave in the first substrate (1) along the fragilisation plane (3). According to the invention, the initiation of the fracture wave is located in a central zone of the fragilisation plane (2) and the propagation speed of this wave is controlled in order to have sufficient speed. In this way, the interactions of the fracture wave with acoustic vibrations emitted during its initiation and/or its propagation are limited to a peripheral zone of the useful layer (3).