Isobutene is prepared by a process in which a) an MTBE-containing stream I is separated by distillation into an MTBE-containing overhead stream II and a bottom stream III which comprises compounds having boiling points higher than that of MTBE; and b) the MTBE present in the overhead stream II is dissociated over a catalyst to give a dissociation product IV; wherein the stream I has a proportion of 2-methoxybutane (MSBE) of greater than 1000 ppm by mass, based on MTBE, and wherein the separation by distillation in step a) and/or the dissociation in step b) is carried out so that the dissociation product IV has a concentration of less than 1000 ppm by mass of linear butenes, based on a C4-olefin fraction.