Air conditioning system for an aircraft cabin , comprising: - a primary exchanger configured to cool bleed air from at least one compressor of the aircraft, - a pre-compressor configured to pre-compress the cooled bleed air, - an intermediate exchanger configured to cool the pre-compressed air from the pre-compressor , - a main compressor configured to receive said pre-compressed bleed air cooled by the intermediate exchanger and compress said air, - a main exchanger configured to cool the compressed bleed air by means of ram air taken from outside the aircraft, and - a water extraction loop that includes a main turbine and is configured to extract water from the cooled, compressed bleed air and supply the cabin of the aircraft, characterized in that it comprises a duct for recovering at least part of the air from the cabin after it has passed through the cabin, and recovered air circulation ducts configured so that the recovered air successively passes through: - a secondary exchanger , the recovered air forming a first cold source in said secondary exchanger for cooling the bleed air again downstream of the main exchanger and upstream of the water extraction loop, - a heat exchanger (14; 20), the recovered air forming a second cold source in said heat exchanger (14; 20) for cooling the bleed air upstream or downstream of the pre-compressor , the heat exchanger either being formed by the intermediate exchanger , with the ram air forming a cold source of the primary exchanger , or being formed by the primary exchanger , with the ram air forming a cold source of the intermediate exchanger , - an energy recovery turbine , the recovered air forming a source of energy after passing through the secondary exchanger and then the heat exchanger (14; 20). - a primary exchanger configured to cool bleed air from at least one compressor of the aircraft, - a pre-compressor configured to pre-compress the cooled bleed air, - an intermediate exchanger configured to cool the pre-compressed air from the pre-compressor , - a main compressor configured to receive said pre-compressed bleed air cooled by the intermediate exchanger and compress said air, - a main exchanger configured to cool the compressed bleed air by means of ram air taken from outside the aircraft, and - a water extraction loop that includes a main turbine and is configured to extract water from the cooled, compressed bleed air and supply the cabin of the aircraft, - a secondary exchanger , the recovered air forming a first cold source in said secondary exchanger for cooling the bleed air again downstream of the main exchanger and upstream of the water extraction loop, - a heat exchanger (14; 20), the recovered air forming a second cold source in said heat exchanger (14; 20) for cooling the bleed air upstream or downstream of the pre-compressor , the heat exchanger either being formed by the intermediate exchanger , with the ram air forming a cold source of the primary exchanger , or being formed by the primary exchanger , with the ram air forming a cold source of the intermediate exchanger , - an energy recovery turbine , the recovered air forming a source of energy after passing through the secondary exchanger and then the heat exchanger (14; 20). <EOS>