A process produces dimethyl ether (DME) from methanol (MeOH). The process includes charging a feed mixture consisting of raw MeOH and a process-internally obtained return flow substantially consisting of unconverted MeOH and reaction water to an MeOH column. The feed mixture is evaporated in the MeOH column to form a first distillate substantially consisting of vaporous MeOH. The first distillate is supplied to a reactor and the MeOH is converted to DME by splitting off water in the reactor so as to form a reaction mixture. The reaction mixture is withdrawn from the reactor, charged to a mixture column and separated into a bottom product substantially consisting of water and a second distillate substantially consisting of DME and MeOH. The second distillate is separated in a DME column into a third distillate substantially consisting of DME, a bottom product consisting essentially of water-poor MeOH, and uncondensable gases discharged overhead. The bottom product is either supplied to a top of the MeOH column or mixed with another bottom product withdrawn from a forerun column.