In a method for liquefying a gas rich in carbon dioxide, the gas is compressed to a first pressure greater than its critical pressure in a compressor to form a compressed gas, the compressed gas is cooled through heat exchange with a refrigerant to a variable temperature to form a cooled compressed gas with a density between 370 and 900 kg/m.sup.3, the cooled compressed gas is cooled at supercritical pressure in a first heat exchanger to a temperature below the critical temperature, the gas cooled below the critical temperature is expanded to a second pressure between 45 and 60 bara to form a diphasic fluid which is separated in a phase separator to form a liquid and a gas, and a liquid portion originating from the phase separator provides cold to the first heat exchanger.