The present invention relates to an air conditioning system (10) for an aircraft cabin (12) with at least one air inlet (14) for supplying air to the cabin (12), at least one air outlet (16) for discharging air from the cabin (12) and at least one compressed-air source (52, 54, 56), which is adapted to provide pressurised fresh air for supplying to the cabin (12) via the at least one air inlet (14). The air conditioning system (10) further comprises a heat exchanger (42) supplied with ram air from a ram air inlet (92) for cooling air from the compressed-air source (52, 54, 56), wherein the heat exchanger (42) is disposed upstream of the air inlet (14) of the cabin (12). It is intended that the air conditioning system (10) comprises a cabin air heat exchanger (100) which is designed to be supplied with air discharged from the cabin (12), wherein the cabin air heat exchanger (100) is disposed downstream of the at least one air outlet (16) and upstream of a point (N) at which fresh air is mixed with air from the cabin (12).