The system for measuring high currents or magnetic fields using a magnetoresistive sensor (80) includes a device for applying a known predetermined magnetic bias field Hbias in a direction such that it has a non-zero component of the field perpendicular to a detection direction of the magnetoresistive sensor (80) that also corresponds to a direction of anisotropy of a layer of the magnetoresistive sensor, a device for measuring the variation in resistance of the magnetoresistive sensor (80) and means for determining the external magnetic field H to be measured from the measured resistance variation, the resistance of the sensor being subjected to a monotonic variation function.