HERA is a highly-redundant transit interferometer with 14,m-diameter parabolic dish elements. We exploit the fact that the Galactic centre transits through the main beam of the telescope to attempt a conventional self-calibration approach to imaging and calibration. The Galactic centre provides a bright source which, we show, can be approximated as a point source sufficiently well to initialise the self-calibration loop and derive initial delays and antenna frequency-independent phases. Subsequent iteration using a more complex sky model derived from the data itself then converges to a reasonable bandpass calibration. The calibration solutions have good stability properties. We show therefore that the conventional self-calibration is a feasible parallel approach in addition to the redundant calibration already planned for HERA. The conventional imaging and calibration is useful as a cross-check to the alternatives being pursued in the HERA project, as a way of quantifying the performance of the hardware on the ground (and potentially identifying problems) and as a route to imaging and removing brighter continuum sources before power spectrum analysis.