Rao (1962) suggested a method for calculating a generalized inverse of an arbitrary matrix and used the method to represent a solution to the set of normal equations obtained in the theory of least squares. This method is similar to that used for calculating the regular inverse of a non-singular matrix (namely, the sweep-out method) developed by Gauss. The resulting inverse is a one-condition g-inverse and possesses many properties which make its use more desirable than other proposed g-inverses.This paper contains a discussion of the properties of this one-condition g-inverse, anAPLprogram for computing the inverse, and some examples demonstrating the use of the program. Finally we show that the four-condition unique Moore-Penrose inverse readily follows by the use of this program.