It is generally accepted that the sigmoidal nature of the haemoglobin-oxygen dissociation curve (ODC) is necessary for efficient oxygen transport in terrestrial vertebrates because it allows large volumes of oxygen to be bound or released for relatively small changes in the partial pressure of oxygen (PO2) in the blood. Furthermore, the amount of oxygen to tissues is increased by hydrogen ions produced from the dissociation of carbon dioxide in solution. The generality of these key features of cooperative oxygen binding and the Bohr effect holds for reptiles, birds and mammals, including representatives with special respiratory requirements for diving, burrowing and living at high altitude. Sphenodon punctatus is the sole surviving representative of the ancient order of 'beakhead' reptiles (order Rhynchocephalia) which were once widely distributed during the Triassic period before the spectacular radiation of dinosaur faunas. We have now investigated the oxygen transporting properties of blood from Sphenodon and find that the ODC is hyperbolic, with a high affinity for oxygen and very small Bohr effect. This combination of characteristics is unique among terrestrial vertebrates and accords with a low demand for oxygen and limited scope for aerobic activity.