The relationship between species and the functional diversity of assemblages is fundamental in ecology because it contains key information on functional redundancy, and functionally redundant ecosystems are thought to be more resilient, resistant and stable. However, this relationship is poorly understood and undocumented for species-rich coastal marine ecosystems. Here, we used underwater visual censuses to examine the patterns of functional redundancy for one of the most diverse vertebrate assemblages, the coral reef fishes of New Caledonia, South Pacific. First, we found that the relationship between functional and species diversity displayed a non-asymptotic power-shaped curve, implying that rare functions and species mainly occur in highly diverse assemblages. Second, we showed that the distribution of species amongst possible functions was significantly different from a random distribution up to a threshold of ∼90 species/transect. Redundancy patterns for each function further revealed that some functions displayed fast rates of increase in redundancy at low species diversity, whereas others were only becoming redundant past a certain threshold. This suggested non-random assembly rules and the existence of some primordial functions that would need to be fulfilled in priority so that coral reef fish assemblages can gain a basic ecological structure. Last, we found little effect of habitat on the shape of the functional-species diversity relationship and on the redundancy of functions, although habitat is known to largely determine assemblage characteristics such as species composition, biomass, and abundance. Our study shows that low functional redundancy is characteristic of this highly diverse fish assemblage, and, therefore, that even species-rich ecosystems such as coral reefs may be vulnerable to the removal of a few keystone species.