The invention relates to a magnetic memory with write inhibit selection and the writing method for same. Each memory element of the invention comprises a magnetic tunnel junction (70) consisting of: a magnetic layer, known as the trapped layer (71), having hard magnetisation; a magnetic layer, known as the free layer (73), the magnetisation of which may be reversed; and an insulating layer (72) which is disposed between the free layer (73) and the trapped layer (71) and which is in contact with both of said layers. The free layer (73) is made from an amorphous or nanocrystalline alloy based on rare earth and a transition metal, the magnetic order of said alloy being of the ferrimagnetic type. The selected operating temperature of the inventive memory is close to the compensation temperature of the alloy.