Fossil discoveries and improved phylogenies, have greatly improved our understanding of the origin of tetrapods, making it possible to reconstruct sequences of character change leading to tetrapod morphologies, and to tentatively identify the genetic basis for some of these changes,. However, progress has centred on the upper part of the Tetrapodomorpha which is occupied by Devonian tetrapods such as Acanthostega,, and Ichthyostega. Few advances have been made in improving our understanding of the lower, `fish' part of the group, beyond establishing Elpistostegalia, Osteolepiformes and Rhizodontida as progressively more primitive constituents. It has not been convincingly confirmed or disproved that the Osteolepiformes, a diverse but structurally uniform group that is central to the debate about tetrapod origins, is monophyletic relative to tetrapods (that is, a single side branch on the tetrapod lineage). The earliest steps of the fish-tetrapod transition have thus remained poorly resolved. Here we present the first detailed analysis of the lower part of the Tetrapodomorpha, based on 99 characters scored for 29 taxa. We show that both the Osteolepiformes as a whole and their constituent group Osteolepididae are paraphyletic to tetrapods (that is, each comprises a section of the tetrapod lineage with several side branches), and that their `uniting characters' are attributes of the tetrapodomorph stem lineage. The supposedly discredited idea of osteolepiforms as tetrapod ancestors is, in effect, supported by our analysis. Tetrapod-like character complexes evolved three times in parallel within the Tetrapodomorpha.