Abstract. During the operational phase of the ROSAT satellite between 1990 and 1998 the X-ray telescope pointed 71 times to the Small Magellanic Cloud (SMC) for observations with the High Resolution Imager (HRI), covering a field of 5• × 5• . From these data a catalogue of 121 discrete X-ray sources was derived. By cross-correlating the source catalogue with the SIMBAD data base and the TYCHO catalogue, the systematic positional error of the HRI source positions could be reduced. In total the X-ray position for 99 HRI sources was corrected yielding positional errors between 1 and 16 . The HRI catalogue was also cross-correlated with the catalogues derived from the ROSAT Position Sensitive Propotional Counter (PSPC) pointings (Kahabka et al. 1999;. For 75 HRI sources PSPC counterparts were found and thus hardness ratios are given. With the help of the information obtained from the cross-correlations 56 HRI sources were identified with objects of known or proposed nature. Four foreground stars, six supernova remnants, four supersoft sources, 12 X-ray binaries, and one AGN were detected by the HRI. Based on the existence of a likely optical counterpart or properties like hardness ratio and X-ray to optical flux ratio, further 15 HRI sources were classified into different source types.