In animal breeding and improvement selection is one of the most important artificial manipulations. Especially, it is obvious theoretically that selection by selection index is very effective and so avidly used for the practical purposes. For the accurate grasp of individual aggregate economic breeding value animals are selected by selection index, In this paper the course of establishment of normal equation for the calculation of selection index by maximizing the correlation coefficient (R_(HI)) between aggregate economic breeding value (H) and selection index value (I) is explained mathematically. I hope it is helpful for understanding, framing or application of selection index equation.