A reading circuit includes, for each bit line of a matrix of memory cells, a controllable switching element which can connect the bit line to a voltage source in response to a control signal applied to a control terminal thereof, a detector stage sensitive to the flow of current through the bit line, and a driving stage including two field-effect transistors connected in the inverter configuration with the input of the inverter connected to the bit line and with the output of the inverter connected to the control terminal of the controllable switching element. In order to charge the capacitance associated with the bit line rapidly but without causing oscillatory phenomena, the driving stage includes circuitry for reducing the gain of the feedback loop formed by the inverter and by the controllable switching element.