The invention relates to a process for obtaining isobutene from an isobutene containing C4-hydrocarbon mixture (1) in a plant comprising an etherification unit (3), a first distillation unit (5), an ether cleavage unit (8) and a second distillation unit (10), the process comprising: (a) contacting the C4-hydrocarbon mixture (1) with a primary alcohol (2) and reacting the mixture with the primary alcohol in the presence of an acidic catalyst to form the corresponding alkyl tert-butyl ether as an intermediate product and diisobutene as a by-product in the etherification unit (3): (b) distilling the reaction mixture (4) from the etherification unit (3) in the first distillation unit (5), a C4-hydrocarbon raffinate being withdrawn as the overhead product (6), the alkyl tert-butyl ether and diisobutene being withdrawn as the liquid or vaporous bottom product (7), and vaporizing the bottom product (7) if it is withdrawn as a liquid: (c) reacting the vaporous bottom product (7) in the presence of an acidic catalyst obtaining isobutene and the primary alcohol as reaction products in the ether cleavage unit (8): (d) distilling the reaction mixture (9) from the ether cleavage unit (8) in the second distillation unit (10), isobutene being withdrawn as the overhead product (11), the primary alcohol and diisobutene being withdrawn as the bottom product (12) and being recycled to the etherification unit (3); the plant further comprising a byproduct separation unit (15) being fed by a bottom purge stream (13) of the first distillation unit (5) and/or by a part of the bottom product of the second distillation unit (10), wherein a diisobutene product stream rich in diisobutene is separated from this feed stream (13, 14).