Air conditioning system for a cabin of an aircraft, comprising: - a device for bleeding air from an air source; - an air cycle turbine engine comprising at least one turbine and an energy-consuming wheel mechanically coupled to one another, said turbine comprising an air inlet and an air outlet that is connected to said cabin in order to be able to supply said cabin with air at a controlled pressure and temperature; - at least one heat exchanger, referred to as the main cooling exchanger , which is arranged in a channel for the circulation of ram air drawn from outside the aircraft, between said air bleed device and said air inlet of said turbine , said main exchanger comprising a primary circuit supplied with a flow of hot air from said air bleed device, and a secondary circuit supplied with said ram air, which forms a flow of cold air for cooling said flow of hot air; - a water extraction loop that is arranged between said main exchanger and said turbine and is designed to extract water from the flow of hot air cooled by said main exchanger which supplies said turbine ; and - a pipe for distributing water extracted by said extraction loop , which pipe extends between said water extraction loop and said ram-air channel , upstream of said main exchanger , in order to be able to spray the water extracted by said water extraction loop , referred to as the spray water, into the ram-air flow of said ram-air channel , characterized in that said system further comprises means for heating the spray water, which means are arranged between said water extraction loop and said ram-air channel , upstream of said main cooling exchanger , so as to allow evaporation of the water sprayed into said ram-air channel , which helps to cool the ram air of said primary circuit of the main exchanger and to ensure cooling of the hot air of said primary circuit of said main exchanger . - a device for bleeding air from an air source; - an air cycle turbine engine comprising at least one turbine and an energy-consuming wheel mechanically coupled to one another, said turbine comprising an air inlet and an air outlet that is connected to said cabin in order to be able to supply said cabin with air at a controlled pressure and temperature; - at least one heat exchanger, referred to as the main cooling exchanger , which is arranged in a channel for the circulation of ram air drawn from outside the aircraft, between said air bleed device and said air inlet of said turbine , said main exchanger comprising a primary circuit supplied with a flow of hot air from said air bleed device, and a secondary circuit supplied with said ram air, which forms a flow of cold air for cooling said flow of hot air; - a water extraction loop that is arranged between said main exchanger and said turbine and is designed to extract water from the flow of hot air cooled by said main exchanger which supplies said turbine ; and - a pipe for distributing water extracted by said extraction loop , which pipe extends between said water extraction loop and said ram-air channel , upstream of said main exchanger , in order to be able to spray the water extracted by said water extraction loop , referred to as the spray water, into the ram-air flow of said ram-air channel , characterized in that said system further comprises means for heating the spray water, which means are arranged between said water extraction loop and said ram-air channel , upstream of said main cooling exchanger , so as to allow evaporation of the water sprayed into said ram-air channel , which helps to cool the ram air of said primary circuit of the main exchanger and to ensure cooling of the hot air of said primary circuit of said main exchanger . <EOS>