A survey for millisecond pulsars in a zone along the southern galactic plane has been carried out at a frequency of 843 MHz using the Molonglo Observatory Synthesis Telescope. The area covered by the survey was from l=255° to l=360°, b=±1° in about 7000 separate pointings. Sampling was at 0.5 ms intervals, giving nominal sensitivity down to pulsar periods of one millise- cond. For longer-period pulsars the limiting sensitivity was about 8mJy for dispersion measures up to 400 cm−3 pc. The relatively high frequency of this survey ensured that any reduction in sensitivity owing to interstellar dispersion and scattering was not serious up to distances corresponding to DM values of about 200 cm−3 pc, allowing the search of a considerable volume for relatively bright millisecond pulsars. No millisecond pulsars were found, although some suspects remain under investigation. One new pulsar with a period 106 ms was discovered and parameters are given for this. The survey shows that luminous millisecond pulsars like PSR 1937+21 are not common objects in the disc of our Galaxy.