The invention relates to a process for preparing 1,3-butadiene from n-butenes, comprising the steps of: A) providing an input gas stream a comprising butanes, 1-butene, 2-butene and isobutene, with or without 1,3-butadiene, from a fluid catalytic cracking plant; B) removing isobutene from the input gas stream a, giving a stream b comprising butanes, 1-butene and 2-butene, with or without 1,3-butadiene; C) feeding the stream b comprising butanes, 1-butene and 2-butene and optionally an, oxygenous gas and optionally water vapor into at least one dehydrogenating zone and dehydrogenating 1-butene and 2-butene to 1,3-butadiene, giving a product gas stream c comprising 1,3-butadiene, butanes, 2-butene and water vapor, with or without oxygen, with low-boiling hydrocarbons, with high-boiling secondary components, with or without carbon oxides and with or without inert gases; D) cooling and compressing the product gas stream c, giving at least one aqueous condensate stream d1 and a gas stream d2 comprising 1,3-butadiene, butanes, 2-butene and water vapor, with or without oxygen, with low-boiling hydrocarbons, with or without carbon oxides and with or without inert gases; Ea) removing uncondensable and low-boiling gas constituents comprising low-boiling hydrocarbons, with or without oxygen, with or without carbon oxides and with or without inert gases, as gas stream e2 from the gas stream d2 by absorbing the C4 hydrocarbons comprising 1,3-butadiene, butanes and 2-butene in an absorbent, giving an absorbent stream laden with C4 hydrocarbons and the gas stream e2, and Eb) subsequently desorbing the C4 hydrocarbons from the laden absorbent stream, giving a C4 hydrocarbon stream e1; F) separating the C4 hydrocarbon stream e1 by extractive distillation with a 1,3-butadiene-selective solvent into a stream f1 comprising 1,3-butadiene and the selective solvent and a stream f2 comprising butanes and 2-butene, wherein at least 90% of the 1-butene present in stream b is converted in step C) and a product stream f2 comprising butanes and 2-butene is obtained in step F.