We have designed a GdCo/Cu/NiFe Giant Magnetoresistance (GMR) trilayer, the magnetoresistance of which does not always depend on the angle between the magnetisations of the electrodes. Using a GdCo ferrimagnetic alloy close to compensation, it was possible to experimentally reach the spin flop field Bsf of the ferrimagnetic layer. Below Bsf , the ferrimagnetic layer behaves as a ferromagnetic l...