An aircraft air conditioning system includes a cyclone unit positioned proximate to at least one discharger, the unit having an inlet opening, which communicates with a fresh air supply line, an intake opening, through which air is sucked in from the aircraft cabin, and at least one outlet opening, which communicates with the at least one discharger. A first, cyclone flow of only fresh air is produced in the cyclone unit during operation of the aircraft air conditioning system, the first cyclone flow tending to draw cabin air into the cyclone unit via the intake opening for mixture with the fresh air, after which a second cyclone flow of the cabin air and fresh air are expelled through the outlet opening and the at least one discharger.