The method includes cooling and liquefying a feed gas stream, separating a stream obtained from the feed gas stream, and recovering a treated gas stream and a natural gas liquid stream. The method further includes compressing the treated gas stream in order to form a compressed treated gas stream, and fractionating the natural gas liquid stream into a plurality of hydrocarbon fractions (28, 30, 32, 33). The method additionally includes withdrawing from the compressed treated gas stream, of a recycle stream, and reintroducing the recycle stream without cooling into the feed gas stream, into the cooled feed gas stream, or into a stream obtained from the cooled feed gas stream upstream of an expander.