In this article, a new mathematical proposal is presented to perform digital multispectral images processing of four primary colors; namely, it shows the method and equations that transform the four-band color space (extension of RGB) into the space of color HSI 4 (HSI color model that depends on four primary colors) and vice versa. The HSI model is widely used to develop image processing algorithms based on human perception of color. At present, there are capture and visualization devices based on four primary colors that is why the information contained in this document will be a valuable mathematical tool in the processing of images in the HSI space. The work is divided into two main parts: direct converting , which is based on an already developed article and what is presented here is an application of this one for the case of four primary colors. The second part, inverse converting , is the most important and new contribution. The effectiveness of the mathematical proposal can be verified with the numerical results presented.