We have used the Australia Telescope Compact Array (ATCA) to make a sensitive (5sigma similar or equal to100 mJy) search for maser emission from the 4765-MHz (2) Pi(1/2) F =1-->0 transition of OH. 55 star formation regions were searched and maser emission with a peak flux density in excess of 100 mJy was detected toward 14 sites, with 10 of these being new discoveries. In addition we observed the 4750-MHz (2) Pi(1/2) F =1-->1 transition towards a sample of star formation regions known to contain 1720-MHz OH masers, detecting marginal maser emission from G348.550-0.979. If confirmed this would be only the second maser discovered from this transition.The occurrence of 4765-MHz OH maser emission accompanying 1720-MHz OH masers in a small number of well-studied star formation regions has led to a general perception in the literature that the two transitions favour similar physical conditions. Our search has found that the presence of the excited-state 6035-MHz OH transition is a much better predictor of 4765-MHz OH maser emission from the same region than 1720-MHz OH maser emission is. Combining our results with those of previous high-resolution observations of other OH transitions we have examined the published theoretical models of OH masers and find that none of them predicts any conditions in which the 1665-, 6035- and 4765-MHz transitions are inverted simultaneously.