The detection of an insulation fault on a network furnished with tappings by a first monitor can be followed by the location and identification of the fault by way of a locator to be placed on the tappings. To satisfy the level-two security, or SIL-2, in which the risk of occurrence of a hazard is decreased by a factor of greater than 100, second means for detecting the insulation fault are installed, to obtain a redundant item of information as regards the insulation resistance of the network, independently of the monitor but associated with a locator.