A person under supervision wears a sensor consisting of at least one accelerometer (31) and a magnetometer (41), oriented in his vertical direction. A fall event is picked up when a significant and rapid oscillation of the acceleration signal coincides with a shift in the ambient magnetic field between two levels (between t=4000 and t=5000). Additional criteria that may also make use of the magnetometer enable the diagnosis to be made, and it is easier and safer to establish this than with accelerometers alone.