The invention relates to a method for removing sulfur-containing contaminants in the form of mercaptans and H2S from natural gas, which may also contain CO2 and higher aliphatic and aromatic hydrocarbons, and recovering elemental sulfur, wherein in a first absorption step the sulfur-containing contaminants are removed from the gas, to form on the one hand a purified gas stream an on the other hand a sour gas, which sour gas is fed to a second absorption step in which the sour gas is separated into an H2S-enriched and mercaptan-reduced first gas stream, which is fed to a Claus plant, followed by a selective oxidation step of H2S to elemental sulfur in the tail gas, and an H2S-reduced, and mercaptan-enriched second gas stream, which second gas stream, if desired after further treatment, is subjected to a selective oxidation of sulfur compounds to elemental sulfur.