The method according to the invention comprises the following steps: - treating a feed stream (12) to obtain a treated gas stream (60); - cooling the treated gas stream (60) in a heat exchanger (34) to form at least one column feed fraction; - introducing each column feed fraction into a distillation column (50); - heating at least one downstream flow (106) coming from the head stream (104) of the column in the heat exchanger (34). The treatment step comprises the formation of an intermediate stream (20) comprising at least 20 mol% of ethylene and at least 20 mol% of carbon monoxide, the method comprising a step for eliminating the carbon monoxide contained in the intermediate stream (20).