A method for the treatment of a gas stream, wherein before the combustion of the gas stream, hydrogen sulfide is separated out of the gas stream in a first absorber by an absorption medium, the treated gas stream purified of hydrogen sulfide is burnt in a combustion apparatus, the carbon dioxide contained in the exhaust gas of the burnt gas stream after combustion is separated in a second absorber by an absorption medium, and the separated hydrogen sulfide and carbon dioxide are separated in at least one desorber from the absorption medium for the regeneration of the latter. The same absorption medium separates the hydrogen sulfide out of the gas stream and the carbon dioxide out of the exhaust gas. A corresponding device for the treatment of a gas stream has a first absorber and a second absorber flow-connected to one another for the exchange of absorption medium.