One would expect that colors of single ink halftones would be reproduced by linear addition of the colors of paper and ink, and consequently their chromaticity coordinates would be on the straight line connecting the colors of the paper and ink. However, it is typically observed that the chromaticity coordinate points of single ink halftones lie on a gentle curve other than on the straight line. This non-linearity suggests an existence of a third primary color that is involved in color reproduction of single ink halftones. This article describes the model in which reflectance spectra of halftones are represented by linear addition of three components, that is, the reflectance of paper, the reflectance of ink, and the reflectance of a third primary color. The reflectance of the third primary color is estimated by calculation from the reflectance of the ink and paper. To estimate the amount of one component, a path fraction of light for the reflectance of paper, a principal component analysis was applied to the reflectance spectra of the printed halftones. The amounts of the other two components can be calculated from the probability theory of the Yule-Nielsen effect. By using the proposed model, the reflectance spectra of the halftones was predicted and compared with the measured reflectance spectra. Results showed that the model was able to describe the non-linearity in color reproduction of the halftones. This model is useful for analyzing the characteristics of the halftone system as well as for describing it.