A method for cryogenic separation of air in an air separation plant (100, 200) having a main air compressor, a main heat exchanger and a distillation column system having a low-pressure column operated at a first pressure level and a high-pressure column operated at a second pressure level, wherein - a feed air stream (a), which comprises all of the feed air fed to the air separation plant (100, 200), is compressed in the main air compressor to a third pressure level which is at least 6 bar above the second pressure level, wherein, of the compressed feed air stream (b), - a first fraction (c) is cooled at least once in the main heat exchanger and expanded from the third pressure level in a first expansion turbine, - a second fraction (d) is cooled at least once in the main heat exchanger and expanded from the third pressure level in a second expansion turbine, and - a third fraction (e) is further compressed to a fourth pressure level using a first turbine booster, to which the third fraction (e) is fed at a temperature level of 0 to 50°C, and using a second turbine booster, cooled at least once in the main heat exchanger and expanded from the fourth pressure level, wherein - air of the first fraction (c) and/or the second fraction (d) and/or the third fraction (e) is fed at the first and/or second pressure level into the distillation column system, characterized in that - the third fraction (e) is further compressed to the fourth pressure level in sequence in a recompressor, which is driven by external energy and not or not exclusively by expansion of a fluid previously compressed in the air separation plant (100, 200), the first turbine booster and the second turbine booster, and - for expanding the third fraction (e) use is made of a dense fluid expander to which the third fraction (e) is fed in the liquid state and at the fourth pressure level. - a feed air stream (a), which comprises all of the feed air fed to the air separation plant (100, 200), is compressed in the main air compressor to a third pressure level which is at least 6 bar above the second pressure level, wherein, of the compressed feed air stream (b), - a first fraction (c) is cooled at least once in the main heat exchanger and expanded from the third pressure level in a first expansion turbine, - a second fraction (d) is cooled at least once in the main heat exchanger and expanded from the third pressure level in a second expansion turbine, and - a third fraction (e) is further compressed to a fourth pressure level using a first turbine booster, to which the third fraction (e) is fed at a temperature level of 0 to 50°C, and using a second turbine booster, cooled at least once in the main heat exchanger and expanded from the fourth pressure level, wherein - air of the first fraction (c) and/or the second fraction (d) and/or the third fraction (e) is fed at the first and/or second pressure level into the distillation column system, characterized in that - the third fraction (e) is further compressed to the fourth pressure level in sequence in a recompressor, which is driven by external energy and not or not exclusively by expansion of a fluid previously compressed in the air separation plant (100, 200), the first turbine booster and the second turbine booster, and - for expanding the third fraction (e) use is made of a dense fluid expander to which the third fraction (e) is fed in the liquid state and at the fourth pressure level.