This method comprises the cooling of the initial natural gas and its introduction into a column for recovering C2+ hydrocarbons. It comprises the recovery of the top stream from the column to form the treated natural gas, and the recovery of the bottom stream from the column for introducing it at a feed level of a fractionating column equipped with a top condenser. The column produces the said C3+ hydrocarbons at the bottom. The method comprises the recovery of the ethane rich stream from an intermediate level of the column located above the said feed level and the production of a secondary reflux stream from the said top condenser refluxed to the top of the recovery column.