Aiming at the problem of negative index in the spectral color space built by means of traditional principal component analysis (PCA), a method of color component prediction based on rotated principal component analysis (RPCA) is proposed, which performs the rotating transformation from initial eigenvectors to a set of all-positive vectors as the physical basis color components while retaining the cumulative ratio of the variance contributions of significant principal components to the original multispectral space to the maximum extent. The rotated column vectors should be also polarized between 0 and 1. The spectral database of Munsell Matte Collection I is used for experiment. The experimental results show that the novel method of prediction not only uncovers the real color components of the target image better but reconstructs the normalized spectra data set with a high colorimetric and spectral accuracy. Thereinto, the colorimetric errors of the four estimated components reconstruction for more than 96 percent of the samples in Munsell Matte Collection I are less than 3 units of color difference acceptable.