Haemoglobin (Hb) is the tetrameric protein molecule that in vertebrate blood transports oxygen from the lungs to the tissues. This function depends on four subunits in the molecule binding cooperatively so that their affinity for oxygen increases as the level of oxygenation increases. X-ray analysis has shown that deoxyhaemoglobin, which has a low oxygen affinity, and oxyhaemoglobin, which has a high oxygen affinity, differ principally in their subunit or quaternary structures, referred to as the T and R states, respectively. As it switches from the T state to the R state during oxygenation, Hb increases its oxygen affinity. However, the structural pathway between deoxy- and oxy-haemoglobin is not known, principally because there has been no accurate structural knowledge of the intermediate states. We report here the crystal structure of T state human Hb in which the alpha chains are oxygenated and the beta subunits are oxygen-free. In this crystal the Hb appears to be in an intermediate state between the unliganded T state and the liganded R state. There is also evidence that the Hb molecule operates by loading and unloading the beta haems and thus the alpha-oxy, beta-deoxy Hb crystal may represent a physiologically important state.