(eng): In this paper, we extend the theory of the combined Shape-Color Affine Moment Invariants (SCAMIs) for recognition of color images, proposed originally by Gong et al. in [3]. Since in the real pictures the shape deformation is always accompanied by the color deformation, it is not sufficient to use the shape invariant or color invariant descriptors only and the use of combined invariants is needed. However, the SCAMIs are not able to recognize images, the color channels of which are linearly dependent or highly correlated. This situation is not rare in practice and is of particular importance in hyper-spectral image analysis, where the spectral bands are highly correlated. We analyze why the SCAMIs fail in such situations, correct the theory and propose a solution to overcome such drawback. Unlike the SCAMIs, the new invariants have in the null-space the constant-zero images only, which leads to a better discrimination power, as demonstrated also on various pictures.