The invention relates to a process for fabricating a multilayer structure that includes bonding a first wafer onto a second wafer, where the first wafer may have a chamfered edge and the bonding interface has an adhesion energy of less than or equal to 1 J/m2, and thinning the first wafer so as to form a transferred layer, where before thinning the first wafer, a step of trimming the edge of the first wafer is carried out using a grinding wheel having a working surface which comprises grit particles with an average size of greater than or equal to 800 mesh or less than or equal to 18 microns, and wherein the trimming step is carried out by lowering the grinding wheel at a rate of descent of greater than or equal to 5 microns per second, such that the descent of the grinding wheel into the first wafer continues to a distance from the bonding interface that is less than or equal to 30 μm.