We present a variant of the restarted Pulay's Direct Inversion in the Iterative Subspace (DIIS) method for efficiently and robustly accelerating the convergence of fixed-point iterations. Specifically, we propose a simple modification of DIIS without any additional parameters, which we refer to as the r-Pulay method. We demonstrate the efficacy of r-Pulay in the context of the Jacobi iteration for solving large linear systems of equations, as well as in the Self Consistent Field (SCF) approach for Density Functional Theory (DFT) calculations. Overall, we find r-Pulay to be an attractive version of the restarted DIIS method. (C) 2015 Elsevier B.V. All rights reserved.