In using the method of successive over-relaxation, two difficulties generally arise. Firstly, the efficiency of the method depends greatly on the accelerating factor used, and for any given problem the optimum value of this factor is not usually known priory to solution of the problem. Secondly, it is difficult to estimate the accuracy of solution at any stage. This paper describes a method of using successive over-relaxation in which successively better estimates of the optimum accelerating factor are obtained during the course of solution. The method also yields satisfactory bounds to the error at any stage.