A method for fractionating a stream of cracked gas from a hydrocarbon pyrolysis installation to obtain an ethylene-rich cut and a stream of fuel having a low C 2 + hydrocarbon content, the method comprising the following steps: - upstream cooling and partial condensation of a stream of raw cracked gas by at least partial heat exchange with a coolant fluid circulating in a first external refrigeration cycle and separation of an upstream liquid in at least one upstream drum to form an intermediate stream of cracked gas pre-cooled to a first temperature; - intermediate cooling and partial condensation of the intermediate stream of cracked gas in at least one intermediate heat exchanger (50, 54) and separation of an intermediate liquid (120, 128) in at least one intermediate separation drum (52, 56) to form a downstream stream of cracked gas cooled to a second temperature lower than the first temperature; - downstream cooling and partial condensation of the downstream stream of cracked gas in at least one downstream heat exchanger to a third temperature lower than the second temperature; - introducing the partially condensed downstream stream of cracked gas obtained from the downstream heat exchanger in a downstream separator; - recovering, at the head of the downstream separator, a high-pressure gas stream of fuel, with a low C 2 + hydrocarbon content, and recovering, at the bottom of the downstream separator, a downstream liquid, with a high C 2 + hydrocarbon content; - passing the high-pressure fuel stream through the downstream exchanger and the intermediate exchanger (50, 54) to form a heated high-pressure fuel stream; - expansion of the reheated high-pressure fuel stream in at least a first dynamic expander to obtain a partially expanded fuel stream; - heating the partially expanded fuel stream through the downstream exchanger and the intermediate exchanger (50, 54); - processing at least one liquid (112, 120, 128) obtained during the upstream cooling, intermediate cooling and downstream cooling steps to form the ethylene-rich cut; the method comprising the following steps: - passage of the partially expanded flow of fuel from the intermediate exchanger (50, 54) into a second dynamic expander to form an expanded stream of fuel; - reheating the expanded fuel stream from the second dynamic expander in the downstream heat exchanger and in the intermediate heat exchanger (50, 54); - compressing the reheated expanded fuel stream in at least one compressor (76A, 76B) coupled to at least one turbo-expander (68A, 70A) of the first dynamic expander and/or the second dynamic expander to form the stream of fuel having a low C 2 + hydrocarbon content; and the thermal power needed to cool the intermediate stream of cracked gas towards the second temperature is provided in the intermediate heat exchanger (50, 54) by heat exchange with the high-pressure fuel stream, by heat exchange with the partially expanded fuel stream and by heat exchange with the expanded fuel stream, without heat exchange with an external coolant fluid circulating in a refrigeration cycle. - upstream cooling and partial condensation of a stream of raw cracked gas by at least partial heat exchange with a coolant fluid circulating in a first external refrigeration cycle and separation of an upstream liquid in at least one upstream drum to form an intermediate stream of cracked gas pre-cooled to a first temperature; - intermediate cooling and partial condensation of the intermediate stream of cracked gas in at least one intermediate heat exchanger (50, 54) and separation of an intermediate liquid (120, 128) in at least one intermediate separation drum (52, 56) to form a downstream stream of cracked gas cooled to a second temperature lower than the first temperature; - downstream cooling and partial condensation of the downstream stream of cracked gas in at least one downstream heat exchanger to a third temperature lower than the second temperature; - introducing the partially condensed downstream stream of cracked gas obtained from the downstream heat exchanger in a downstream separator; - recovering, at the head of the downstream separator, a high-pressure gas stream of fuel, with a low C 2 + hydrocarbon content, and recovering, at the bottom of the downstream separator, a downstream liquid, with a high C 2 + hydrocarbon content; - passing the high-pressure fuel stream through the downstream exchanger and the intermediate exchanger (50, 54) to form a heated high-pressure fuel stream; - expansion of the reheated high-pressure fuel stream in at least a first dynamic expander to obtain a partially expanded fuel stream; - heating the partially expanded fuel stream through the downstream exchanger and the intermediate exchanger (50, 54); - processing at least one liquid (112, 120, 128) obtained during the upstream cooling, intermediate cooling and downstream cooling steps to form the ethylene-rich cut; - passage of the partially expanded flow of fuel from the intermediate exchanger (50, 54) into a second dynamic expander to form an expanded stream of fuel; - reheating the expanded fuel stream from the second dynamic expander in the downstream heat exchanger and in the intermediate heat exchanger (50, 54); - compressing the reheated expanded fuel stream in at least one compressor (76A, 76B) coupled to at least one turbo-expander (68A, 70A) of the first dynamic expander and/or the second dynamic expander to form the stream of fuel having a low C 2 + hydrocarbon content; and