A system for producing biomethane comprising: - at least one module for producing biogas (F0), - at least one scrubbing unit capable of separating the biogas stream coming from the at least one module for producing biogas into a stream of biomethane (F1) and a stream of residual gases (F2) containing a proportion of methane, - at least one module for combusting residual gases characterised, on the one hand, by a so-called "methane" factor (Y CH4 mini manufacturer ) denoting the minimum volume fraction of methane that said stream of residual gases (F2) has to contain to allow combustion of methane it contains and, on the other hand, by a so-called "dioxygen" factor (λ) denoting the minimum amount of dioxygen to be fed to be able to burn said residual gases, - at least one supply module capable of supplying a gaseous stream comprising dioxygen to the at least one module for combusting residual gases, said system being characterised in that : - it comprises a control module capable of determining the volume fraction of methane (Y residual CH4 ) of the stream of residual gases (F2), of calculating a dioxygen-enrichment rate (Y O2 enriched air ) of an air stream (F3) for performing combustion of methane contained in said residual gases in the combustion module from the volume fraction of methane (Y residual CH4 ) of the stream of residual gases (F2) determined by respecting the dioxygen factor (λ) and the methane factor (Y CH4 mini manufacturer ) of the combustion module , and of sending the dioxygen-enrichment rate (Y O2 enriched air ) calculated to the at least one supply module , - the at least one supply module is capable of generating a gaseous stream (F4) comprising a proportion of dioxygen equal to the dioxygen-enrichment rate (Y O2 enriched air ) received from the control module . - at least one module for producing biogas (F0), - at least one scrubbing unit capable of separating the biogas stream coming from the at least one module for producing biogas into a stream of biomethane (F1) and a stream of residual gases (F2) containing a proportion of methane, - at least one module for combusting residual gases characterised, on the one hand, by a so-called "methane" factor (Y CH4 mini manufacturer ) denoting the minimum volume fraction of methane that said stream of residual gases (F2) has to contain to allow combustion of methane it contains and, on the other hand, by a so-called "dioxygen" factor (λ) denoting the minimum amount of dioxygen to be fed to be able to burn said residual gases, - at least one supply module capable of supplying a gaseous stream comprising dioxygen to the at least one module for combusting residual gases, - it comprises a control module capable of determining the volume fraction of methane (Y residual CH4 ) of the stream of residual gases (F2), of calculating a dioxygen-enrichment rate (Y O2 enriched air ) of an air stream (F3) for performing combustion of methane contained in said residual gases in the combustion module from the volume fraction of methane (Y residual CH4 ) of the stream of residual gases (F2) determined by respecting the dioxygen factor (λ) and the methane factor (Y CH4 mini manufacturer ) of the combustion module , and of sending the dioxygen-enrichment rate (Y O2 enriched air ) calculated to the at least one supply module , - the at least one supply module is capable of generating a gaseous stream (F4) comprising a proportion of dioxygen equal to the dioxygen-enrichment rate (Y O2 enriched air ) received from the control module . <EOS>