An absorption medium contains a dissolved amino acid salt and a dissolved metal. The absorption medium is brought into contact with the acidic gas in an absorber. In the absorber, the H2S goes over from the gas phase into the liquid phase. In addition, carbon dioxide (CO2) is likewise absorbed from the gas as a function of the contact time. The scrubbing solution is conveyed from the absorber into a regeneration tank. In the regeneration tank, the solution is treated with air, with oxygen (O2)-enriched air or with pure O2. As a result of the introduction of O2 into the solution, the H2S present in the solution is reacted at the dissolved metal catalyst. After the regeneration, possible solids are separated off and the regenerated scrubbing solution is recirculated to the absorber.