We have analysed radio-continuum mosaics of the Small Magellanic Cloud (SMC) obtained using both the Australia Telescope Compact Array (ATCA) and the Parkes telescope and present a new catalogue of sources in the SMC at 1.42, 2.37, 4.80 and 8.64GHz ({lambda}=20, 13, 6 and 3cm). We find a total of 717 radio-continuum sources at these frequencies in the field of the SMC, which is three times more than previous Parkes surveys. From these 717 radio-continuum sources, some 534 were detected at 1.42GHz, 697 at 2.37GHz, 75 at 4.80GHz and 54 at 8.64GHz. The integrated flux density was measured for each of these sources. We have assessed the accuracy of the position and flux measurements of our catalogue and found no significant discrepancy with previous catalogues. Our new data show a significant improvement in sensitivity (over 10 times) and positional accuracy (<1") over previous catalogues.