The invention relates to an air conditioning system for conditioning the air of a passenger space of a motor vehicle, the system including a refrigerant circuit with a compressor, a first heat exchanger for the heat exchange between the refrigerant and the environment and a second heat exchanger for supplying heat from the refrigerant to the air supply to be conditioned for the passenger space. The refrigerant circuit further includes, in the flow direction of the refrigerant after the compressor, a valve arrangement. The valve arrangement comprises a branch, a first valve arranged between the branch and the second heat exchanger, and a second valve arranged between the branch and the first heat exchanger. The first valve is designed with a normally open (NO) valve characteristic and the second valve with a normally closed (NC) valve characteristic.