The relationship between global trait distinctiveness and geographic range size is an emerging pattern of interest in macroecology. Early observations suggested that the relationship was positive, implying that globally widespread species hold the rarest combinations of traits. Here, we formally describe and test the relationship in the world's birds and consider its implications for global functional diversity and redundancy. We demonstrate that the relationship is best described as triangular with a positive upper boundary, with its linear model significance lost when including phylogenetic effects. The triangular relationship is formed by groups of phylogenetically related widespread species with moderate and high trait distinctiveness. Decomposing the relationship further using quantile regression highlights the unique traits of these widespread birds. Overall, the triangular relationship emphasises that while not all widespread species have rare trait combinations, those that do should not be overlooked in conservation efforts, regardless of their current threat status.