Disclosed is a method for treating a feed gas stream rich in hydrogen sulfide by partially combusting the feed gas stream rich in hydrogen sulfide with an oxygen-enriched gas in a Claus reaction furnace to produce to a combustion reaction product stream containing sulfur. The combustion reaction product stream is split into a recycle stream and a treatment stream and the recycle stream directed back into the Claus reaction furnace, without first condensing sulfur out of the recycle stream, while the treatment stream is directed into a condenser to condense sulfur out of the treatment stream.