The present invention relates to a method for producing an aromatic hydrocarbon from a C1-C4-alkane, or a mixture of C1-C4-alkanes, which comprises a) bringing a feedstock stream A which comprises a C1-C4-alkane, or a mixture of C1-C4-alkanes, into contact with a catalyst and reacting a part of the C1-C4-alkane, or a part of the mixture of the C1-C4-alkanes, to form aromatic hydrocarbon(s); b) fractionating the product stream B resulting from step a) into a low-boiler stream C which comprises the majority of the hydrogen and of the unreacted C1-C4-alkane, or of the mixture of C1-C4-alkanes, and a high-boiler stream D, or a plurality of high-boiler streams D′, which stream or streams comprises or comprise the majority of the aromatic hydrocarbon formed; and c) feeding the low-boiler stream C to a further C1-C4-alkane-consuming method, if appropriate the hydrogen present in the low-boiler stream C being separated off in advance.