This method comprises: forming an expanded intermediate recirculation stream (170) from a liquid (112, 128) obtained during an upstream cooling and/or intermediate cooling step, upstream from the downstream cooling step; circulating the intermediate recirculation stream (170) at least in an upstream heat exchanger (42) to cool an upstream stream of cracked gas (102); reintroducing the reheated intermediate recirculation stream (170) in a raw cracked gas (20) upstream from at least one compressor (36, 38) of a cooling and compression stage (24). The upstream, intermediate and downstream cooling steps is carried out without a heat exchanger respectively of an upstream stream of cracked gas (102), an intermediate stream of cracked gas (114) and a downstream stream of cracked gas (140) with an external refrigeration cycle.