An iterative method was developed by Hawkyard in 1993 for generating reflectance functions, based on a given set of tristimulus values. In a recent article by Dupont (Col Res Appl 2002;27:88-99), many methods for generating reflectance functions were compared, and it was shown that the Hawkyard method is one of the best methods. However, one of the weak points of the Hawkyard method is its iterative nature. In addition, one important issue for the Hawkyard method is its convergence, which has not been addressed. In this article, this issue is examined. The necessary and sufficient condition to achieve convergence, using the Hawkyard method, is given. The method is then modified to make it an analytical method. (c) 2005 Wiley Periodicals, Inc.