A method for producing a methane-rich stream and a C 2 + hydrocarbon-rich fraction from a dehydrated feed natural-gas stream, consisting of hydrocarbons, nitrogen and of CO 2, advantageously having a C 2 + hydrocarbon molar content of more than 10%, the method being of the type comprising the following steps: - cooling the feed natural-gas stream, advantageously at a pressure of more than 40 bars, in a first heat exchanger, and introducing the cooled feed natural-gas stream into a separator flask; - separating the cooled natural gas stream in the separator flask and recovering an essentially gaseous light fraction and an essentially liquid heavy fraction; - forming a turbine input flow from the light fraction; - dynamically expanding the turbine input flow in a first expansion turbine, and introducing the expanded flow into an intermediate portion of a splitter column; - expanding the heavy fraction and introducing the heavy fraction into the splitter column, the heavy fraction recovered in the separator flask being introduced into the splitter column without passing through the first heat exchanger; - recovering, at the foot of the splitter column, a C 2 + hydrocarbon-rich bottom stream intended to form the C 2 + hydrocarbon-rich fraction; - sampling at the head of the splitter column a methane-rich head stream; - heating up the methane-rich head stream in a second heat exchanger and in the first heat exchanger and compressing this stream in at least one first compressor coupled with the first expansion turbine and in a second compressor in order to form a methane-rich stream from the compressed methane-rich head stream; - sampling in the methane-rich head stream (82, 84, 86) a first recirculation stream; - passing the first recirculation stream into the first heat exchanger and into the second heat exchanger in order to cool it down, and then introducing at least one first portion of the cooled recirculation stream into the upper portion of the splitter column; - forming at least one second recirculation stream (96; 136; 168; 192) obtained from the methane-rich head stream downstream from the splitter column; characterized in that the method includes the following steps: - forming a dynamic expansion stream (100; 136) from the second recirculation stream (96; 136; 168; 192) and introducing the dynamic expansion stream (100; 136) into an expansion turbine (22; 132) in order to produce frigories; and in that the second recirculation stream is introduced into a stream (40; 46) located downstream from the first heat exchanger and upstream from the first expansion turbine in order to form the dynamic expansion stream. - cooling the feed natural-gas stream, advantageously at a pressure of more than 40 bars, in a first heat exchanger, and introducing the cooled feed natural-gas stream into a separator flask; - separating the cooled natural gas stream in the separator flask and recovering an essentially gaseous light fraction and an essentially liquid heavy fraction; - forming a turbine input flow from the light fraction; - dynamically expanding the turbine input flow in a first expansion turbine, and introducing the expanded flow into an intermediate portion of a splitter column; - expanding the heavy fraction and introducing the heavy fraction into the splitter column, the heavy fraction recovered in the separator flask being introduced into the splitter column without passing through the first heat exchanger; - recovering, at the foot of the splitter column, a C 2 + hydrocarbon-rich bottom stream intended to form the C 2 + hydrocarbon-rich fraction; - sampling at the head of the splitter column a methane-rich head stream; - heating up the methane-rich head stream in a second heat exchanger and in the first heat exchanger and compressing this stream in at least one first compressor coupled with the first expansion turbine and in a second compressor in order to form a methane-rich stream from the compressed methane-rich head stream; - sampling in the methane-rich head stream (82, 84, 86) a first recirculation stream; - passing the first recirculation stream into the first heat exchanger and into the second heat exchanger in order to cool it down, and then introducing at least one first portion of the cooled recirculation stream into the upper portion of the splitter column; - forming at least one second recirculation stream (96; 136; 168; 192) obtained from the methane-rich head stream downstream from the splitter column; - forming a dynamic expansion stream (100; 136) from the second recirculation stream (96; 136; 168; 192) and introducing the dynamic expansion stream (100; 136) into an expansion turbine (22; 132) in order to produce frigories; and in that the second recirculation stream is introduced into a stream (40; 46) located downstream from the first heat exchanger and upstream from the first expansion turbine in order to form the dynamic expansion stream.