A modification to Broyden’s method for obtaining stable and computationally efficient convergence in self-consistent calculations is developed and discussed. The method incorporates the advantages of two schemes proposed by Srivastava and by Vanderbilt and Louie without any increase in complexity. Its improvement over their methods is discussed. The present method is compared with two other widely used convergence methods, simple mixing and Anderson’s method, for the case of the disordered binary alloy Ni0.35Fe0.65 on the verge of a magnetic instability and is shown to be much improved in stability and rate of convergence.