A method for supplying air to an engine of an aircraft via an air supply system of the aircraft. A dynamic air intake vent of the system can be closed by a closure member that is movable between a closed position and an open position. A static air intake vent is equipped with a filter medium. During flight, the method comprises an unfiltered operating mode that comprises the following steps: positioning of the closure member in the open position, and, during a phase of forward travel of the aircraft, dynamic intake of a flow of air, then transfer of a first portion of the flow of air to the engine and a second portion of the flow of air to the filter medium in order to clean the filter medium.