Abstract: A method for the processing, by separation technology, of a product stream (g), containing at least dimethyl ether, methanol, water, carbon dioxide, carbon monoxide and hydrogen, from a reactor (4) used for the synthesis of dimethyl ether (z) from synthesis gas (e), is proposed. The product stream (g) is fed, in at least partially gaseous form, into an absorption column (6) operated with a liquid reflux, a gaseous top stream (m) being removed from the absorption column (6) at the top and a liquid sump stream (p) being removed at the bottom. The sump stream (p) is at least partially fed into a first distillation column (5), a gaseous transfer stream (q) containing dimethyl ether and a stream (r) predominantly containing methanol and/or water being removed from the first distillation column (5).