A new species of squalid shark, Squalus asper, is described from the equatorial western Indian Ocean. It is characterized the form of the dermal denticles, the blades of which are at least three times longer than any reported from other similar sized individuals of the genus. The horizontal and vertical distribution of S. asper is indicated. The relation of S. asper with other species of Squalus is discussed and, in particular, the morphology of the new species is compared with that of four specimens of S. blainvillei collected in the same area at the same time. The two species are also shown to be clearly segregated taxonomically on the basis of a cluster analysis on 49 normalized sets of common morphometric measurements. A similar comparison was made between S. asper and the other generally accepted species groups of the genus, based upon 26 normalized sets of data common to both the currently reported specimens and 16 others quoted in the literature. S. asper is shown to be clearly distinct, although the overall pattern indicated by the dendrograms of speciation within the genus is somewhat confused. The validity of such taxonomic groupings is speculated upon.