Electrical breakdown sets a limit on the kinetic energy that particles in a conventional radio-frequency accelerator can reach. New accelerator concepts must be developed to achieve higher energies and to make future particle colliders more compact and affordable. The plasma wakefield accelerator (PWFA) embodies one such concept, in which the electric field of a plasma wake excited by a bunch of charged particles (such as electrons) is used to accelerate a trailing bunch of particles. To apply plasma acceleration to electron-positron colliders, it is imperative that both the electrons and their antimatter counterpart, the positrons, are efficiently accelerated at high fields using plasmas(1). Although substantial progress has recently been reported on high-field, high-efficiency acceleration of electrons in a PWFA powered by an electron bunch(2), such an electron-driven wake is unsuitable for the acceleration and focusing of a positron bunch. Here we demonstrate a new regime of PWFAs where particles in the front of a single positron bunch transfer their energy to a substantial number of those in the rear of the same bunch by exciting a wakefield in the plasma. In the process, the accelerating field is altered-'self-loaded'-so that about a billion positrons gain five gigaelectronvolts of energy with a narrow energy spread over a distance of just 1.3 metres. They extract about 30 per cent of the wake's energy and form a spectrally distinct bunch with a root-mean-square energy spread as low as 1.8 per cent. This ability to transfer energy efficiently from the front to the rear within a single positron bunch makes the PWFA scheme very attractive as an energy booster to an electron-positron collider.