A process for producing an olefin having N carbon atoms is proposed in which using a dehydrogenation a process gas is formed which contains at least the olefin having N carbon atoms, a paraffin having N carbon atoms and a hydrocarbon having N−1 carbon atoms and in which using at least a portion of the process gas a separation input is formed which is subjected to a low temperature separation in which the separation input is cooled stepwise over a plurality of temperature levels and condensates are separated from the separation input, wherein the condensates are at least partly subjected to a first low temperature rectification to obtain a first gas fraction and a first liquid fraction, wherein the first gas fraction contains at least the olefin having N carbon atoms in a lower proportion than in the condensates and the hydrocarbon having N−1 in a higher proportion than in the condensates. It is provided that the first gas fraction is at least partly subjected to a second low temperature rectification using a liquid reflux containing predominantly or exclusively the hydrocarbon having N−1 carbon atoms in which the first gas fraction undergoes depletion in the olefin having N carbon atoms. A corresponding plant (100) likewise forms part of the subject matter of the invention.