The letter describes a simple and useful extension of existing theory on the determination of optimum accelerating factor for successive over-relaxation applied to solutions of Laplace's and Poisson's equations. In particular, domains where the condition ∂φ/∂n= 0 is applied along part of the boundaiy contour are considered. The boundary along which this condition is applied need not be linear. © 1969, The Institution of Electrical Engineers. All rights reserved.