CIE colorimetry based on colour matching functions has been successfully applied in various industrial applications. In the past it was generally accepted that the chromaticity diagram based on either 1931 or 1964 colour matching functions (CMFs), contains all the chromaticity coordinates of stimuli, which means the domain (𝛺) enclosed by the spectrum locus and the purple line is convex. Also based on the chromaticity diagram, the Helmholtz coordinates (dominant wavelength and excitation purity) can be defined. In this paper, these properties of chromaticity coordinates based on CIE 1931, CIE 1964, CIE 2006 2- and 10-degree cone fundamentals (CFs) and cone fundamentals-based CMFs are evaluated. It is found that the domain 𝛺 does not contain the chromaticity coordinates of all stimuli, and spectral chromaticity coordinates do not distribute in the wavelength order along the spectrum locus, which results in no way to determine the Helmholtz coordinates for certain stimuli. Finally modified CIE 1931 CMFs, CIE 1964 CMFs, and CFs and CMFs based on CFs, are derived.