THE centre of our Galaxy is known to contain a large condensation of mass(1), and it has been suggested that a massive black hole (of several million solar masses) is located there. Massive black holes have been proposed to explain active galactic nuclei, and if the Galactic Centre is a less-powerful version of such sources it should radiate X-rays and gamma-rays(1). But although earlier observations(2-6) have shown that the region does emit X-rays and gamma-rays, the true centre, corresponding to the object Sagittarius A*, does not emit strongly at least up to energies of 30 keV (refs 4-6). Whether Sgr A* emits radiation at higher energies, however, was not resolved. Here we present the results of a deep imaging survey of the Galactic Centre, performed with the Sigma/GRANAT telescope. We determine the locations of the nine hard X-ray sources-six of them being observed for the first time in the spectral band-to an accuracy of about 2 arcmin, but find no source associated with Sgr A*. The hard X-ray luminosity of Sgr A* is a factor of. 4 x 10(7) less than that expected for a black hole of a million solar masses accreting gas at the maximum stable rate, challenging the idea that there is a black hole at the Galactic Centre.