This paper discusses about the most different illuminant (termed the orthogonal illuminant) compared with a reference illuminant. This is the first report on the definition of the orthogonal illuminant and on the solution of the optimization problem. As an application, the orthogonal illuminant is applied to derive the optimized spectral reflectance for color constancy. No reports have appeared about the optimization for color constancy because of the lack of such models as the orthogonal illuminant. In experiments, the solution of the orthogonal illuminant and the solution of the optimized spectral reflectance for color constancy are indicated and discussed.