THE first example of a new type of transient X-ray source recently appeared in the direction of the Galactic Centre(1), During the peak of its outburst, the new source, GRO J1744 - 28, was very bright in X-rays(2) and produced both 2.1-Hz periodic pulsations(3) and intense bursts lasting tens of seconds(1,4). Before the discovery of this source, it was thought that X-ray stars could not display these different types of activity simultaneously. Here we discuss the nature of the source, which seems to be a strongly magnetic neutron star accreting matter from a low-mass companion star in a low-inclination orbit. The dipole component of its magnetic field is less than or similar to 10(11) G. When the source was at its brightest, its X-ray luminosity between bursts was close to the Eddington critical luminosity(5), at which the outward force of the escaping radiation balances the inward force of gravity. The X-ray bursts probably occur when matter that has accumulated in the inner part of the accretion disk briefly overcomes the forces that oppose its inflow, and the gas falls onto the neutron star.