A method for conditioning an aircraft, including the following steps: - providing an autonomous electricity production and conditioning system for an aircraft, including: * a rotary shaft; * a compressor mounted integral with the rotary shaft; * a power turbine capable of rotating the rotary shaft; * a cold expansion turbine rotated by the rotary shaft and supplied with a compressed gas from the compressor; * an upstream assembly supplying outside air to the aircraft not having passed through a propulsion engine (16A, 16B) of the aircraft, the upstream supply assembly being connected to an inlet of the compressor, * a main alternator mechanically connected to the rotary shaft, * a secondary alternator separate from the main alternator, the secondary alternator being mechanically connected to the rotary shaft; the method comprising the following steps: - activating the power turbine to rotate the rotary shaft; - jointly rotating the compressor and the expansion turbine; - supplying the compressor with air outside the aircraft not having passed through a propulsion engine (16A, 16B) of the aircraft, the activating step comprising a starting step of the autonomous system, in which an electric network of the aircraft comprising batteries is electrically connected to the auxiliary alternator to supply said alternator and cause it to operate as an engine, then a deactivation step of the auxiliary alternator when the power turbine rotates the shaft independently, such that when the shaft is rotated, the main alternator operate as a generator and provides electric power to the electric network of the aircraft. - providing an autonomous electricity production and conditioning system for an aircraft, including: * a rotary shaft; * a compressor mounted integral with the rotary shaft; * a power turbine capable of rotating the rotary shaft; * a cold expansion turbine rotated by the rotary shaft and supplied with a compressed gas from the compressor; * an upstream assembly supplying outside air to the aircraft not having passed through a propulsion engine (16A, 16B) of the aircraft, the upstream supply assembly being connected to an inlet of the compressor, * a main alternator mechanically connected to the rotary shaft, * a secondary alternator separate from the main alternator, the secondary alternator being mechanically connected to the rotary shaft; the method comprising the following steps: * a rotary shaft; * a compressor mounted integral with the rotary shaft; * a power turbine capable of rotating the rotary shaft; * a cold expansion turbine rotated by the rotary shaft and supplied with a compressed gas from the compressor; * an upstream assembly supplying outside air to the aircraft not having passed through a propulsion engine (16A, 16B) of the aircraft, the upstream supply assembly being connected to an inlet of the compressor, * a main alternator mechanically connected to the rotary shaft, * a secondary alternator separate from the main alternator, the secondary alternator being mechanically connected to the rotary shaft; the method comprising the following steps: - activating the power turbine to rotate the rotary shaft; - jointly rotating the compressor and the expansion turbine; - supplying the compressor with air outside the aircraft not having passed through a propulsion engine (16A, 16B) of the aircraft,