A method for modulating a valve regulating the flow rate of gas towards a burner is presented. The valve with the associated closure member configured to operate with a predetermined characteristic curve, the flow rate delivered being proportionally related to the strength of a first current signal sent to the modulator such that the flow rate can be modulated, using the proportionality, within a range of modulation between a maximum flow rate and a minimum flow rate. To deliver controlled gas flow rates that are below the minimum flow rate, the modulator is driven with a second PWM voltage signal capable of generating a particular second PWM current signal, to move the closure member of the valve according to the second signal. First and second time intervals correspond to successive durations of high signal and low signal, respectively, the sum being equal to a period of the second signal.