A process for the purification of isobutene from a C4 stream with at least 1-butene, 2-butene, isobutane and isobutene includes isomerizing 1-butene from a stream of material which is concentrated in isobutane and isobutene obtained from the C4 stream into 2-butene, using a catalyst in an isomerization reactor; supplying a product stream from the isomerization reactor to a rectification column; and providing a stream of material which is concentrated in isobutene. A processing facility is utilized for the purification of isobutene from the C4 stream.