A process for purifying a recycle stream from a 1,3-butadiene processing plant, comprising - 70-99% by weight of 1,3-butadiene, based on the total weight of the recycle stream, - 0.1-10% by weight of low boilers relative to 1,3-butadiene, based on the total weight of the recycle stream, and - 0.1-20% by weight of high boilers relative to 1,3-butadiene, based on the total weight of the recycle stream, where the sum of 1,3-butadiene, low boilers and high boilers in the recycle stream is 100% by weight and the starting material is a pure 1,3-butadiene feedstream having a 1,3-butadiene content of greater than 98% by weight of 1,3-butadiene, based on the total weight of the pure 1,3-butadiene feedstream, which is subjected beforehand to a prepurification for removal of high boilers relative to 1,3-butadiene in a stripping column and is then supplied to the 1,3-butadiene processing plant, which comprises dividing the recycle stream into two substreams, specifically into - a first substream which is purified in the stripping column for prepurification of the pure 1,3-butadiene feedstream to obtain a first purified recycle stream also comprising the prepurified pure 1,3-butadiene feedstream, and - a second substream which is purified in an extractive distillation plant by extractive distillation with a selective solvent, said extractive distillation plant comprising - a main scrubber which is in the form of a rectifying column and to which are fed in liquid form the second substream of the recycle stream in the lower region and the selective solvent in the upper region, the selective solvent flowing through the main scrubber in countercurrent to the second substream of the recycle stream and becoming laden with 1,3-butadiene, and from which a top stream comprising butanes and butenes is discharged, and - an outgasser column to which the bottom stream from the main scrubber is supplied, and from which a second purified recycle stream overhead, and a bottom stream comprising purified selective solvent are drawn off, and the first purified recycle stream and the second purified recycle stream being recycled into the 1,3-butadiene processing plant, with the proviso that the recycle stream is divided in such a way that a maximum flow rate is accounted for by the first substream while complying with the specifications for the sum of all streams fed into the 1,3-butadiene processing plant, of a proportion of 1,3-butadiene of greater than or equal to 90% by weight, based on the total weight of all C 4 hydrocarbons from the sum of all streams fed into the 1,3-butadiene processing plant. - 70-99% by weight of 1,3-butadiene, based on the total weight of the recycle stream, - 0.1-10% by weight of low boilers relative to 1,3-butadiene, based on the total weight of the recycle stream, and - 0.1-20% by weight of high boilers relative to 1,3-butadiene, based on the total weight of the recycle stream, where - a first substream which is purified in the stripping column for prepurification of the pure 1,3-butadiene feedstream to obtain a first purified recycle stream also comprising the prepurified pure 1,3-butadiene feedstream, and - a second substream which is purified in an extractive distillation plant by extractive distillation with a selective solvent, said extractive distillation plant comprising - a main scrubber which is in the form of a rectifying column and to which are fed in liquid form the second substream of the recycle stream in the lower region and the selective solvent in the upper region, the selective solvent flowing through the main scrubber in countercurrent to the second substream of the recycle stream and becoming laden with 1,3-butadiene, and from which a top stream comprising butanes and butenes is discharged, and - an outgasser column to which the bottom stream from the main scrubber is supplied, and from which a second purified recycle stream overhead, and a bottom stream comprising purified selective solvent are drawn off, and the first purified recycle stream and the second purified recycle stream being recycled into the 1,3-butadiene processing plant, with the proviso that the recycle stream is divided in such a way that a maximum flow rate is accounted for by the first substream while complying with the specifications for the sum of all streams fed into the 1,3-butadiene processing plant, of a proportion of 1,3-butadiene of greater than or equal to 90% by weight, based on the total weight of all C 4 hydrocarbons from the sum of all streams fed into the 1,3-butadiene processing plant. - a main scrubber which is in the form of a rectifying column and to which are fed in liquid form the second substream of the recycle stream in the lower region and the selective solvent in the upper region, the selective solvent flowing through the main scrubber in countercurrent to the second substream of the recycle stream and becoming laden with 1,3-butadiene, and from which a top stream comprising butanes and butenes is discharged, and - an outgasser column to which the bottom stream from the main scrubber is supplied, and from which a second purified recycle stream overhead, and a bottom stream comprising purified selective solvent are drawn off, and