The process comprises the following steps: - taking a recycling stream (152) from a top stream (131, 140, 141) resulting from a recovery column (35); - causing heat exchange between the recycling stream (152) and at least one part of the top stream (131) resulting from the recovery column (35), - reintroducing, after expansion, the cooled and expanded recycling stream into the recovery column (35). The process comprises taking at least one bottom reboiling stream (165) from the bottom of the recovery column (35), and causing heat exchange between the bottom reboiling stream and at least a part of the starting natural gas (13) and/or the recycling stream (152), wherein the bottom reboiling is provided by the heat taken from the starting natural gas stream (13) and/or from the recycling stream (152).
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