To confirm faint Be/X-ray binary candidates from the XMM-Newton survey of the Small Magellanic Cloud, we searched for X-ray outbursts in archival ROSAT observations. We found that RXJ0123.4-7321 was much brighter when detected with ROSAT than seen 16 years later by XMM-Newton. We analysed the ROSAT observations and the OGLE I-band light curve of the optical counterpart to investigate the nature of the system. High long-term variability in the X-ray flux of a factor of ∼150 was found between the ROSAT and XMM-Newton detections, indicating strong outburst activity during the ROSAT observations. The I-band light curve reveals long-term variability and regular outbursts with a period of (119.9±2.5) days, indicating the orbital period of the binary system. The large X-ray flux variations and the properties of the optical counterpart confirm RXJ0123.4-7321 as a new Be/X-ray binary in the wing of the Small Magellanic Cloud.