The risk of inbreeding is particularly high in small, closed, and isolated populations of island endemic species because there are few opportunities for gene flow to introduce novel alleles from other populations. One of the mechanisms that may facilitate inbreeding avoidance within populations is sex-biased dispersal, which results in close kin of the opposite sex not being in the same area for breeding. Here we investigated natal and breeding dispersal to determine sex-bias, post-dispersal breeding outcomes, and the effects of bird density on dispersal in the endemic Chatham Island black robin (Petroica traversi). Studies on island species in a closed environment where no immigration or emigration occurs, offer a unique opportunity to distinguish between emigration and mortality, which is a main challenge for dispersal studies. We found that natal dispersal in black robins was significantly female-biased in both proportion of birds dispersing and the distance dispersed. Bird density in the natal year increased the likelihood of juvenile dispersal of both sexes. Dispersal between successive breeding seasons was rare; when it occurred it was significantly female-biased in the proportion of birds dispersing but not in the distance dispersed. Regardless of sex, black robins were more likely to disperse after losing a mate, but females dispersed further than males after mate loss. Dispersal negatively impacted breeding success with dispersing black robins having lower breeding success post-dispersal than birds that did not disperse. This study suggests that sex-biased density-dependent dispersal – and not kin recognition – is the default mechanism that avoids pairings between close relatives in this species.