Using a steam lance (16), the water vapor and compressed air are supplied to the milk via two pipelines (21, 22) which are separated from one another up to the outlet from the steam lance, wherein only steam is supplied through the outer pipeline (21) at a vapor velocity necessary for breaking up the protein molecules of the milk, whereas a steam-air mixture is supplied through the inner pipeline (22) to enrich the milk with the necessary air proportion, and is only mixed with the steam from the outer pipeline (22) in the milk to be frothed. The steam lance (16) is composed of the two pipelines (21, 22) arranged coaxially to one another, and an end piece (23) which separates them from one another in the outlet area and has outlet openings (24, 25) for the two media, the steam and the steam-air mixture, designed as radial nozzles which are inclined horizontally and also relative to one another.
