Method for producing transistors of the N-channel type and transistors of the P-channel type in an initially tensilely stressed substrate of the fully depleted silicon on insulator type comprising an initially tensilely stressed silicon semiconductor film disposed on a "buried" insulating layer itself disposed on an unstressed silicon supporting substrate, the method comprising a localised modification of the stresses comprising: a formation of at least one opening in the initially stressed silicon semiconductor film and in the underlying buried insulating layer until the unstressed silicon substrate has been reached, said opening being formed at a well intended to allow contact with the silicon supporting substrate from the upper face of the initially stressed silicon semiconductor film, an epitaxy of silicon in said at least one opening starting from the unstressed silicon supporting substrate in such a way as to fill said at least one opening, forming at least one zone of unstressed epitaxied silicon, a localised amorphisation of a zone of said initially stressed silicon semiconductor film including said at least one zone of unstressed epitaxied silicon, forming at least one amorphised zone, and a recrystallisation of said at least one amorphised zone by a solid-phase epitaxy starting from the part of said at least one zone of unstressed epitaxied silicon located in said at least one opening and in contact with said at least one amorphised zone, in such a way as to obtain in the initially stressed silicon semiconductor film at least one localised zone of film including tensilely destressed silicon, a production of insulation zones, in such a way as to electrically insulate zones of the initially stressed silicon semiconductor film including tensilely stressed silicon and said at least one localised zone of film including tensilely destressed silicon and define said well, the method further comprising: a production of the P-channel transistors in said at least one localised zone of tensilely destressed silicon, and a production of the N-channel transistors in the zones of the initially stressed silicon semiconductor film including tensilely stressed silicon. a formation of at least one opening in the initially stressed silicon semiconductor film and in the underlying buried insulating layer until the unstressed silicon substrate has been reached, said opening being formed at a well intended to allow contact with the silicon supporting substrate from the upper face of the initially stressed silicon semiconductor film, an epitaxy of silicon in said at least one opening starting from the unstressed silicon supporting substrate in such a way as to fill said at least one opening, forming at least one zone of unstressed epitaxied silicon, a localised amorphisation of a zone of said initially stressed silicon semiconductor film including said at least one zone of unstressed epitaxied silicon, forming at least one amorphised zone, and a recrystallisation of said at least one amorphised zone by a solid-phase epitaxy starting from the part of said at least one zone of unstressed epitaxied silicon located in said at least one opening and in contact with said at least one amorphised zone, in such a way as to obtain in the initially stressed silicon semiconductor film at least one localised zone of film including tensilely destressed silicon, a production of insulation zones, in such a way as to electrically insulate zones of the initially stressed silicon semiconductor film including tensilely stressed silicon and said at least one localised zone of film including tensilely destressed silicon and define said well, the method further comprising: a production of the P-channel transistors in said at least one localised zone of tensilely destressed silicon, and a production of the N-channel transistors in the zones of the initially stressed silicon semiconductor film including tensilely stressed silicon. a production of the P-channel transistors in said at least one localised zone of tensilely destressed silicon, and a production of the N-channel transistors in the zones of the initially stressed silicon semiconductor film including tensilely stressed silicon.