The late Telychian (Silurian: Llandovery) graptolite Monograptus nodifer Törnquist, 1881 has long been problematical, in part because Törnquist’s original material is missing and there has been doubt as to whether the specimens he subsequently described as nodifer in 1892 were of the same species. We conclude that the 1881 and 1892 descriptions refer to the same species, and propose a neotype from Törnquist’s original material. We demonstrate that nodifer shows markedly biform thecal character. The proximal thecae are essentially streptograptid. Growth of the ventral metathecal wall parallel to the protheca then heralds an abrupt change to the distal thecal style, which is characterized by tight, double recurvature, with a flange made of a further extension of the ventral metathecal wall; the new genus Awarograptus is created to encompass this remarkable morphology. Derivation was almost certainly from a streptograptid graptolite, by the distal introduction of a new thecal character. The biform thecal character might have had a reproductive, rather than hydrodynamic or feeding purpose.