A catalogue is presented based on the radio positions of 436 extragalactic sources distributed over the entire sky. The positional accuracy of the sources is better than 3 milliarcsec (mas) in both coordinates, with the majority of the sources having errors better than 1mas. This catalogue is based upon a general solution of all applicable dual frequency 2.3 and 8.4GHz Mark-III VLBI data available through the end of 1993 consisting of 1,015,292 pairs of group delay and phase delay rate observations. Details and positions are also given for an additional 124 objects that either need further observation or are currently unsuitable for the definition of a reference frame. The final orientation of the catalogue has been obtained by a rotation of the positions into the system of the International Earth Rotation Service and is consistent with the FK5 J2000.0 optical system, within the limits of the link accuracy.