1. Over the last 30 years there has been a great deal of interest in investigating patterns of species co-occurrence across a number of locations, which has led to the development of numerous methods to determine whether there is evidence that a particular pattern may not have occurred by random chance. 2. A key aspect that seems to have been largely overlooked is the possibility that species may not always be detected at a location when present, which leads to 'false absences' in a species presence/absence matrix that may cause incorrect inferences to be made about co-occurrence patterns. Furthermore, many of the published methods for investigating patterns of species co-occurrence do not account for potential differences in the site characteristics that may partially (at least) explain non-random patterns (e.g. due to species having similar/different habitat preferences). 3. Here we present a statistical method for modelling co-occurrence patterns between species while accounting for imperfect detection and site characteristics. This method requires that multiple presence/absence surveys for the species be conducted over a reasonably short period of time at most sites. The method yields unbiased estimates of probabilities of occurrence, and is practical when the number of species is small (< 4). 4. To illustrate the method we consider data collected on two terrestrial salamander species, Plethodon jordani and members of the Plethodon glutinosus complex, collected in the Great Smoky Mountains National Park, USA. We find no evidence that the species do not occur independently at sites once site elevation has been allowed for, although we find some evidence of a statistical interaction between species in terms of detectability that we suggest may be due to changes in relative abundances.