Process for distilling a gas mixture of CO2 and at least one component lighter than CO2, containing the following steps: i) compressing the gas mixture in a compressor to produce a gas mixture to be cooled ii) cooling and partial or total condensation of the gas mixture to be cooled so as to obtain a CO2-enriched liquid flow iii) sending the CO2-enriched liquid flow or a liquid flow formed by enriching the enriched liquid flow even more in CO2 to an upper part of a distillation column so as to separate said liquid flow into a gas enriched in the at least one lighter component and depleted in CO2 at the top of the column and a CO2-rich liquid at the bottom of the column, the distillation column comprising an upper part, a lower part, a top and a bottom iv) sending a CO2-enriched gas flow to the bottom of the column so as to generate an upflow in the column v) extracting a CO2-depleted gas stream at the top of the column vi) extracting a CO2-rich liquid product at the bottom of the column, characterized in that the process contains the following steps: vii) extracting a partially purified liquid CO2 stream at an intermediate level of the column at least one theoretical plate below the top of the column and at least one theoretical plate above the bottom of the column viii) heating and vaporizing at least part of the stream extracted at the intermediate level of the column to form a vaporized stream by heat exchange with the gas mixture that cools in step ii) and ix) compressing at least part of the vaporized stream in the compressor with the gas mixture. i) compressing the gas mixture in a compressor to produce a gas mixture to be cooled ii) cooling and partial or total condensation of the gas mixture to be cooled so as to obtain a CO2-enriched liquid flow iii) sending the CO2-enriched liquid flow or a liquid flow formed by enriching the enriched liquid flow even more in CO2 to an upper part of a distillation column so as to separate said liquid flow into a gas enriched in the at least one lighter component and depleted in CO2 at the top of the column and a CO2-rich liquid at the bottom of the column, the distillation column comprising an upper part, a lower part, a top and a bottom iv) sending a CO2-enriched gas flow to the bottom of the column so as to generate an upflow in the column v) extracting a CO2-depleted gas stream at the top of the column vi) extracting a CO2-rich liquid product at the bottom of the column, characterized in that the process contains the following steps: vii) extracting a partially purified liquid CO2 stream at an intermediate level of the column at least one theoretical plate below the top of the column and at least one theoretical plate above the bottom of the column viii) heating and vaporizing at least part of the stream extracted at the intermediate level of the column to form a vaporized stream by heat exchange with the gas mixture that cools in step ii) and ix) compressing at least part of the vaporized stream in the compressor with the gas mixture. vii) extracting a partially purified liquid CO2 stream at an intermediate level of the column at least one theoretical plate below the top of the column and at least one theoretical plate above the bottom of the column viii) heating and vaporizing at least part of the stream extracted at the intermediate level of the column to form a vaporized stream by heat exchange with the gas mixture that cools in step ii) and ix) compressing at least part of the vaporized stream in the compressor with the gas mixture.