Process for isolating pure 1,3-butadiene from a crude C4 fraction by extractive distillation using a selective solvent, wherein (a) the crude C4 fraction is introduced into a predistillation column, a first low boiler fraction comprising C3-hydrocarbons is taken off as overhead stream, a gaseous C4 fraction is taken off as side stream and a first high boiler fraction is taken off as bottom stream, (b) the gaseous C4 fraction is brought into contact with a selective solvent in at least one extraction column, giving an overhead fraction comprising butanes and butenes and a bottom fraction comprising 1,3-butadiene and selective solvent, (c) crude 1,3-butadiene is desorbed from the bottom fraction in at least one stripping column, with a stripped selective solvent being obtained and the stripped selective solvent being recirculated to the extraction column, and (d) at least part of the crude 1-3-butadiene is fed to a pure distillation column and a second high boiler fraction is separated off and a gaseous purge stream is taken off. Gaseous purge streams from the columns which are necessary in order to keep the concentration of molecular oxygen below a predetermined concentration limit are consolidated with output streams which are in any case provided for discharging other components in the process. The recirculation of the second high boiler fraction to a lower section of the predistillation column creates a further degree of freedom in operation of the pure distillation column.