The paper deals with the problem of a construction of opponent functions, which stem from the linear summation of three receptor (R, G, B) signals. It is considered two stages model: stage of the receptors and stage of the opponent cells. Each stage has the own intrinsic independent generators of noise. The colour is determined by the point in three-dimensional space with coordinates {xi}, (i=l, 2, 3), where xi is value of the output signals of the opponent cells. Let V be the volume of “colour body” and be the volume of sphere, where an end of a colour vector is located with a given probability P0. Then a ratio V/s characterizes a colour discriminability: the greater ratio V/s the greater discriminability of the system. It is looking for such transformation of receptor signals into opponent those (i.e. searching a linear operator A), that the ratio V/s would be maximal. The properties of the proposed model were investigated. They fit well to the properties obtained in traditional psychophysical experiments: opponent colour functions, hue coefficients, wavelength and saturation discrimination, achromatic channel sensitivity, non-additivity of brightness. This led to conclusion that the possible role of the colour opponency is ensuring optimal colour discriminability in human vision.