The invention relates to a method of processing measurement signals from a movement senor on board a motor vehicle, according to which, initially, and in a preliminary phase, a reference value AcOff, called offset value, is stored, representative of the value of the signal output by the movement sensor, with the vehicle stopped, a so-called noise value Bb representative of the white noise of said sensor, and an acceleration value Sa determining a running threshold of the motor vehicle. Then, according to this method, and throughout the life of the vehicle, sequences of n successive measurements are taken of the value Ac(t) of the signal output by the movement sensor, and, for each of these sequences, the stored offset value AcOff is subtracted from each of the n measured value and each of the duly calculated values is compared with the stored running threshold, and information representative of a stopped state of the vehicle is transmitted if, and only if, the n calculated values are all less than the stored running threshold and roughly equal to each other with a tolerance margin corresponding to the stored noise value.