Shell small, thin, high spired. Protoconch of 2 whorls, smooth, glossy, 0.62 mm high, 0.80 mm wide. Remainder of shell 5 whorls, each with 8-9 low, gently curving varix-like ribs which line up on adjacent whorls. Distinct growth lines present. Aperture ovate, lip thickened by varix. Anterior canal short, broad. Sutures moderately indented. Colour off-white with faint brown band across whorl which can be seen through aperture.

C. costatus is of about the same size and close in shell characters to C. undatus, but although he described both, Hedley (1922) did not compare the two. The two species come from very different localities, with C. costatus described from the tropical waters off Darnley I. and C undatus from temperate waters off Sydney. In addition to being geographically separated, close examination shows several characters by which the two species can be separated. C. undatus has a much larger, domed protoconch and thinner, wavy axial ribs which do not match on adjacent whorls. C. costatus has very fine spiral striae which are absent on C. undatus.

Type locality: 146 m depth, 35 km east of Narrabeen, Sydney, NSW.
Distribution: Previously known only from 146-183 m off New South Wales, but now also known from Western Australia.