A control device for a switching converter having an input terminal, an output terminal, a semi-bridge of a first and second transistor coupled between the input terminal and a reference voltage, includes a first circuit for driving the first transistor and a second circuit for driving the second transistor. The converter further includes a bootstrap circuit for powering the first drive circuit. The bootstrap circuit includes a capacitor coupled between a supply voltage and the common terminal of the first and second transistors. The control device acts upon the second transistor to assure the charging of the capacitor.