The invention relates to a resistive memory (5) including resistive elements, the resistance of each resistive element being capable of alternating between a high value in a first range of values and a low value in a second range of values smaller than the high value, the memory further comprising a device (14) for switching the resistance of at least one resistive element selected from among the resistive elements between the high and low values, the device including a first circuit capable of applying an increasing voltage across the selected resistive element while the selected resistive element is at the high value or at the low value, a second circuit capable of detecting the switching of the resistance of the selected resistive element, and a third circuit capable of interrupting the current flowing through the selected resistive element on detection of the switching.