Following the discovery by Quashnock and Lamb of an apparent excess of gamma-ray burst pairs with small angular separations, we reanalyse the angular distribution of the bursts in the BATSE catalogue. We find that, in addition to an excess of close pairs, there is also a comparable excess of antipodal bursts, i.e. pairs of bursts separated by about 180 degrees in the sky. Both excesses are moderately significant. Quashnock and Lamb argue that the excess of burst pairs with small angular separations is evidence that many bursts repeat, but obviously this hypothesis cannot explain the excess of antipodal coincidences. Since the two excesses have similar characteristics, and since we cannot think of any physical model of bursts that can produce antipodal pairs, we suggest that both excesses may be due to some unknown selection effect.