A method for simultaneously producing a treated natural gas, a cut rich in C 3 + hydrocarbons and under at least certain production conditions, an ethane-rich stream, from an initial natural gas stream containing methane, ethane and C 3 + hydrocarbons, the method comprising the following steps: - cooling and partly condensing the initial natural gas stream in at least one first upstream heat exchanger in order to form a cooled initial stream; - separating the cooled initial gas stream into a liquid flow and a gas flow; - expanding the liquid flow, and introducing a stream stemming from the liquid flow into a column for recovering C 2 + hydrocarbons at a first intermediate level; - forming a stream for feeding a turbine from the gas flow; - expanding the feed stream in a dynamic expansion turbine and introducing it into the recovery column at a second intermediate level; - recovering and compressing at least one portion of the head stream of the recovery column in order to form the natural gas and recovering the foot stream of the recovery column in order to form a C 2 + -hydrocarbon-rich liquid stream; - introducing the liquid stream at a feed level of a fractionation column provided with a head condenser, the ethane-rich stream being produced under said production conditions, from a stream stemming from the fractionation column, the fractionation column producing a foot stream intended to at least partly form the C 3 + hydrocarbon cut; - introducing a primary reflux stream produced in the head condenser with reflux into the fractionation column; - producing a secondary reflux stream from the head condenser and introducing the secondary reflux stream at the head of the recovery column, characterized in that the method includes the following steps: - sampling a recycling stream in the head stream (131, 140, 141) stemming from the recovery column; - establishing a heat exchange relationship of the recycling stream with at least one portion of the head stream stemming from the recovery column, - reintroducing, after expansion, the cooled and expanded recycling stream into the recovery column, the method including the sampling in the bottom of the recovery column of at least one bottom reboiling stream, and establishing a heat exchange relationship of the bottom reboiling stream with at least one portion of the initial natural gas or/and with the recycling stream, the bottom reboiling being ensured by the calories taken from the initial natural gas stream or/and from the recycling stream - cooling and partly condensing the initial natural gas stream in at least one first upstream heat exchanger in order to form a cooled initial stream; - separating the cooled initial gas stream into a liquid flow and a gas flow; - expanding the liquid flow, and introducing a stream stemming from the liquid flow into a column for recovering C 2 + hydrocarbons at a first intermediate level; - forming a stream for feeding a turbine from the gas flow; - expanding the feed stream in a dynamic expansion turbine and introducing it into the recovery column at a second intermediate level; - recovering and compressing at least one portion of the head stream of the recovery column in order to form the natural gas and recovering the foot stream of the recovery column in order to form a C 2 + -hydrocarbon-rich liquid stream; - introducing the liquid stream at a feed level of a fractionation column provided with a head condenser, the ethane-rich stream being produced under said production conditions, from a stream stemming from the fractionation column, the fractionation column producing a foot stream intended to at least partly form the C 3 + hydrocarbon cut; - introducing a primary reflux stream produced in the head condenser with reflux into the fractionation column; - producing a secondary reflux stream from the head condenser and introducing the secondary reflux stream at the head of the recovery column, - sampling a recycling stream in the head stream (131, 140, 141) stemming from the recovery column; - establishing a heat exchange relationship of the recycling stream with at least one portion of the head stream stemming from the recovery column, - reintroducing, after expansion, the cooled and expanded recycling stream into the recovery column,