The skull and lower jaw of a new sphenodontid reptile Diphydontosaurus avonis is described from disarticulated bones. The fossils were recovered from a detrital limestone of Rhaetian age deposited within solutional and tectonically formed fissures within the Carboniferous Limestone of Tytherington quarry near Bristol. The bone remains, numbering over 1000, are exquisitely preserved with intact facets. Diphydontosaurus was the smallest member of an insular fauna, was primarily insectivorous, and probably formed locally high-density populations. Uniquely for a sphenodontid, Diphydontosaurus had pleurodont teeth on the premaxilla and on the anterior regions of the dentary and maxilla. However, Diphydontosaurus also has the series of acrodont teeth alternating in size on the maxilla and dentary which is characteristic of the Sphenodontidae and particularly Sphenodon. An analysis of 49 synapomorphs in the Diapsida emphasises the sphenodontid nature of Diphydontosaurus. A study of these synapomorphs among the other Triassic sphenodontids Clevosaurus and Planocephalosaurus and the eosuchian Gephyrosaurus suggests that the lack of a quadrate-quadratojugal conch and the complete lower temporal bar are secondarily derived in the `living fossil' Sphenodon punctatus. The tuatara is therefore much less archaic than hitherto proposed. Functional reasons are advocated for the loss of the conch and the regrowth of a complete lower temporal bar. Transformation series are described which could have led to the shape of the maxilla, dentary, premaxilla, palatine and to the loss of the lacrimal in Sphenodon.