A process for preparing isobutene including cleaving a mixture obtained from an MTBE-containing feedstock and/or an MTBE-containing stream, affording a stream of reaction products consisting of isobutene, methanol, MTBE and by-products, the latter consisting of a1) high boilers having a boiling range above 55° C. at a pressure of 0.1 MPa; a2) medium boilers having a boiling range of 12 to 55° C. at a pressure of 0.1 MPa; and a3) low boilers having a boiling range below 12° C. at a pressure of 0.1 MPa; distillatively separating into a stream which contains the isobutene product and low boilers, and a stream which contains MTBE, methanol, medium boilers and high boilers; distillatively separating to obtain an MTBE-containing stream and a methanol-containing high boiler stream; recycling an MTBE-containing stream in which the medium boilers being removed completely or partially before recycling.