We report the discovery in the Galactic Centre region of two hard X-ray sources, designated as XMM J174457−2850.3 and XMM J174544−2913.0, which exhibit flux variations in the 2–10 keV band in excess of a factor of 100 in observations spanning roughly a year. In both cases the observed hydrogen column density is consistent with a location near to the Galactic Centre, implying peak X-ray luminosities of ∼5 × 1034 erg s-1. These objects may represent a new population of transient source, with properties very different from those of the much more luminous Galactic Centre transients associated with neutron star and black hole binary systems. Spectral analysis shows that XMM J174457−2850.3 has relatively weak iron-line emission set against a very hard continuum. XMM J174544−2913.0, on the other hand, has an extremely strong K-line from helium-like iron with an equivalent width of ∼2.4 keV. The nature of the latter source is of particular interest. Does it represent an entirely new class of object or does it correspond to a known class of source in a very extreme configuration?s