The switching converter mainly includes a duty cycle controller (DCC) whose output controls a switch (T1) for transferring energy from an input (VIN) to an output (VOUT). DCC includes a sawtooth generator (ST) and a pulse generator (NL) whose output signals (STO, NLO) are OR-ed and then compared with an error voltage (VE), derived from the output voltage (VOUT) and a reference voltage (VREF1), so as to produce an output signal the duty cycle of which linearly varies from a predetermined non-zero value onwards, thus ensuring that during each cycle T1 is activated for a minimum duration.