We compared unique and other constant hue loci measured at a fixed retinal illuminance for the same observers. When expressed in Judd chromaticity coordinates, unique hue and constant hue data agreed. Unique blue loci were curved, and unique red and green loci were noncollinear. These data imply that unique hues are not a linear transformation of color matching functions. Linear models are only an approximation, even at a single luminance level.