This paper describes a special-purpose matrix inversion technique developed in the System-Planning Branch of TVA (Tennessee Valley Authority). This is the first known use of the method. It is particularly applicable to the inversion of matrices that describe power system impedances or admittances. As outlined, the technique is not entirely general. It requires division by elements of the major diagonal. Thus, when the element is being used as a divisor, it must not be zero. Under such a condition the digital program changes the sequence of calculations. However, a zero in the final diagonal position to be used will cause the matrix to be considered singular. The technique can be made more general but this is not necessary for most power system work.