Brill [Color Res Appl 2006;31:142-145] and Brill and Susstrunk [Color Res Appl 2008;33:424-426] found that CIECAM02 has the yellow-blue and purple problems and gave partial solutions to them. In this article we model the optimum solution to the yellow-blue and purple problems simultaneously as a constrained non-linear optimization problem. An optimum solution resulting in a new CAT02 matrix is numerically obtained. This new matrix satisfies the nesting rule and performs better than the Hunt-Pointer-Estevez (HPE) matrix in predicting both corresponding colours and colour appearance data sets. Specifically, it was found that the new and HPE matrices performed significantly different on nine (out of 21) corresponding colour data sets and on all corresponding colours data sets as a whole. (c) 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 491-503, 2015