A corollary of Grassman's linearity law is formally derived, and states: If a number of colors have a corresponding color appearance A in different illuminants, then their complementary colors have a corresponding color appearance B. The informal logic is that: (1) a perceived color has only one complementary color; (2) two or more corresponding colors have the same complementary color (given the illuminant whites are a color match); so (3) the complementary colors to corresponding colors will themselves be a set of corresponding colors. A method of predicting corresponding colors is derived theoretically and shown to agree with data. (c) 2005 Wiley Periodicals, Inc.