A secure system for charging a battery of a motor vehicle from a power supply network, which system is in a vehicle and includes a mechanism measuring frequency of the network, an injection mechanism injecting current pulses into the network, a mechanism measuring voltage between the ground and a neutral of the network, an analog filter filtering the measured voltages at high frequencies, a digital filter filtering the analog-filtered voltages at low frequencies, and a mechanism determining resistance between the ground and the neutral of the network on the basis of the digitally filtered voltages and an amplitude of the current pulses. The digital filter includes a mean value filter which determines a mean value based on N voltage measurements spaced apart by a time interval T+T/N, where T is the period of the network determined by the mechanism measuring the frequency of the network.