Air conditioning system for a cabin of an aircraft, the air conditioning system comprising: a pressurized air source which, when in its operative mode, provides work air with a pressure higher than 100 kPa; a cooling air source, suitable for providing cooling air; a main heat exchanger with a cold side and a hot side, the hot side comprising an inlet and an outlet and the cold side comprising an inlet and an outlet, in such a way that the inlet of the cold side of the main heat exchanger is in fluid communication with the cooling air source, and the inlet of the hot side of the main heat exchanger is in fluid communication with the pressurized air source; a secondary duct which bleeds part of the air, from the outlet of the cold side of the main heat exchanger; or from the inlet of the cold side of the main heat exchanger, a first valve configured to allow or restrict the pass of air bled to the secondary duct; mixing means and a compressor with an inlet and an outlet, the inlet of the compressor being located in fluid communication with, the outlet of the cold side of the main heat exchanger or the inlet of the cold side of the main heat exchanger, a second valve being located in fluid communication with the outlet of the compressor; wherein the outlet of the compressor is in fluid communication with the mixing means which in turn are adapted to be in fluid communication with the cabin, wherein the mixing means comprise a manifold, comprising at least one inlet (61, 62) and at least one outlet (63, 64), wherein at least one inlet of the manifold is in fluid communication with the outlet of the compressor, each inlet (61, 62) of the manifold comprising a third valve (32, 33); a mixing chamber comprising at least one inlet and at least one outlet (72, 73), one of the inlets of the mixing chamber being fed by the outlet of the hot side of the main heat exchanger, and the at least one outlet (72, 73) of the mixing chamber being adapted to be in fluid communication with the cabin; wherein at least an outlet (63, 64) of the manifold is in fluid communication with an outlet (72, 73) of the mixing chamber, this outlet (63, 64) of the manifold comprising a fourth valve (34, 35); and wherein each outlet (72, 73) of the mixing chamber is adapted to be in fluid communication with the cabin. a pressurized air source which, when in its operative mode, provides work air with a pressure higher than 100 kPa; a cooling air source, suitable for providing cooling air; a main heat exchanger with a cold side and a hot side, the hot side comprising an inlet and an outlet and the cold side comprising an inlet and an outlet, in such a way that the inlet of the cold side of the main heat exchanger is in fluid communication with the cooling air source, and the inlet of the hot side of the main heat exchanger is in fluid communication with the pressurized air source; a secondary duct which bleeds part of the air, from the outlet of the cold side of the main heat exchanger; or from the inlet of the cold side of the main heat exchanger, a first valve configured to allow or restrict the pass of air bled to the secondary duct; mixing means and a compressor with an inlet and an outlet, the inlet of the compressor being located in fluid communication with, the outlet of the cold side of the main heat exchanger or the inlet of the cold side of the main heat exchanger, a second valve being located in fluid communication with the outlet of the compressor; a manifold, comprising at least one inlet (61, 62) and at least one outlet (63, 64), wherein at least one inlet of the manifold is in fluid communication with the outlet of the compressor, each inlet (61, 62) of the manifold comprising a third valve (32, 33); a mixing chamber comprising at least one inlet and at least one outlet (72, 73), one of the inlets of the mixing chamber being fed by the outlet of the hot side of the main heat exchanger, and the at least one outlet (72, 73) of the mixing chamber being adapted to be in fluid communication with the cabin;