Process for the preparation of dimethyl ether product by catalytic conversion of synthesis gas to dimethyl ether comprising the steps of contacting a stream of synthesis gas comprising carbon dioxide in a dimethyl ether synthesis step in one or more reactors and with one or more catalysts active in the formation of methanol and dehydration of methanol to dimethyl ether and forming a product mixture comprising dimethyl ether, carbon dioxide and unconverted synthesis gas; cooling and separating the product mixture into a first liquid phase comprising dimethyl ether and carbon dioxide being dissolved in the formed dimethyl ether, and into a first gaseous phase comprising unconverted synthesis gas containing carbon monoxide and carbon dioxide; passing the first liquid phase to a scrubbing zone and contacting the phase with a liquid sorbent being effective in absorption of carbon dioxide; and withdrawing a dimethyl ether product being depleted in carbon dioxide from the scrubbing zone.