A method for transferring a useful layer to a carrier substrate comprises: joining a front face of a donor substrate to a carrier substrate along a bonding interface to form a bonded structure; annealing the bonded structure to apply a weakening thermal budget thereto and bring a buried weakened plane in the donor substrate to a defined level of weakening, the anneal reaching a maximum hold temperature; and initiating a self-sustained and propagating splitting wave in the buried weakened plane by applying a stress to the bonded structure to lead to the useful layer being transferred to the carrier substrate. The initiation of the splitting wave occurs when the bonded structure experiences a thermal gradient defining a hot region and a cool region of the bonded structure, the stress being applied locally in the cool region, and the hot region experiencing a temperature lower than the maximum hold temperature.