The calculation of colour distances in the first quadrant of the CIEDE2000 space can be realized now after the author succeeded in working out such calculations in the CIE94 and CMC space in preceeding articles. The new system is presented and then the Euclidean line element is established, from which terms are derived for the new coordinates of lightness, hue, and hue angle. The calculations of colour distances are carried out with the new Euclidean coordinates according to a well-known method and are demonstrated by examples guided by CIE94 and CMC distances from the preceeding articles. Finally, proposals are given for the eventual improvement of the CIEDE2000 formula. (C) 2005 Wiley Periodicals, Inc.