A method for fractionating a stream of cracked gas from a hydrocarbon pyrolysis plant to obtain an ethylene-rich cut and a C 2 + hydrocarbon-lean fuel stream, the method comprising the following steps: - compression of the stream of raw cracked gas in a first compressor, and in a second compressor of a cooling and compression stage to form a compressed cracked gas stream; - upstream cooling and partial condensation, in at least one upstream heat exchanger, of an upstream stream of cracked gas, obtained from the compressed cracked gas stream, and separation of an upstream liquid in at least one upstream balloon to form an intermediate stream of cracked gas pre-cooled at first temperature; - intermediate cooling and partial condensation of the intermediate stream of cracked gas in an intermediate heat exchanger and separation of an intermediate liquid in an intermediate separating balloon 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; - introduction of the downstream stream of partially condensed cracked gas from the downstream heat exchanger in a downstream separator; - recovery, at the head of the downstream separator, of a gas stream of high-pressure fuel, lean in C 2 + hydrocarbons, and recovery, at the bottom of the downstream separator, of a downstream liquid, rich in C 2 + hydrocarbons; - passage of the stream of high-pressure fuel through the downstream exchanger and the intermediate exchanger to form a heated high-pressure fuel stream; - expansion of the heated high-pressure fuel stream in at least one first dynamic expansion device to obtain a stream of partially expanded fuel; - heating of the stream of partially expanded fuel through the downstream exchanger and the intermediate exchanger; - treatment of at least one liquid stream obtained during the upstream cooling, intermediate cooling and downstream cooling steps to form the ethylene-rich cut; characterized in that the method comprises the following steps: - forming an expanded intermediate recirculation stream from a liquid (112, 128) obtained during the upstream cooling and/or intermediate cooling steps, upstream from the downstream cooling step; - circulating the intermediate recirculation stream at least in the upstream heat exchanger to cool the upstream stream of cracked gas; - reintroducing the reheated intermediate recirculation stream in the raw cracked gas between the first compressor and the second compressor of the cooling and compression stage, the upstream, intermediate and downstream cooling steps being carried out without heat exchange respectively of the upstream stream of cracked gas, the intermediate stream of cracked gas and the downstream stream of cracked gas with an external refrigeration cycle, such as an ethylene cycle, and in that the pressure of the expanded intermediate recirculation stream is greater than 15% of the pressure of the compressed cracked gas stream. - compression of the stream of raw cracked gas in a first compressor, and in a second compressor of a cooling and compression stage to form a compressed cracked gas stream; - upstream cooling and partial condensation, in at least one upstream heat exchanger, of an upstream stream of cracked gas, obtained from the compressed cracked gas stream, and separation of an upstream liquid in at least one upstream balloon to form an intermediate stream of cracked gas pre-cooled at first temperature; - intermediate cooling and partial condensation of the intermediate stream of cracked gas in an intermediate heat exchanger and separation of an intermediate liquid in an intermediate separating balloon 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; - introduction of the downstream stream of partially condensed cracked gas from the downstream heat exchanger in a downstream separator; - recovery, at the head of the downstream separator, of a gas stream of high-pressure fuel, lean in C 2 + hydrocarbons, and recovery, at the bottom of the downstream separator, of a downstream liquid, rich in C 2 + hydrocarbons; - passage of the stream of high-pressure fuel through the downstream exchanger and the intermediate exchanger to form a heated high-pressure fuel stream; - expansion of the heated high-pressure fuel stream in at least one first dynamic expansion device to obtain a stream of partially expanded fuel; - heating of the stream of partially expanded fuel through the downstream exchanger and the intermediate exchanger; - treatment of at least one liquid stream obtained during the upstream cooling, intermediate cooling and downstream cooling steps to form the ethylene-rich cut; - forming an expanded intermediate recirculation stream from a liquid (112, 128) obtained during the upstream cooling and/or intermediate cooling steps, upstream from the downstream cooling step; - circulating the intermediate recirculation stream at least in the upstream heat exchanger to cool the upstream stream of cracked gas; - reintroducing the reheated intermediate recirculation stream in the raw cracked gas between the first compressor and the second compressor of the cooling and compression stage,