{"references": ["A. Hadjidimos, A. Psimarni, A. K. Yeyios, \"On the convergence of the modified accelerated overrelaxation (MAOR) method,\" Applied Numerical Mathematics, vol.10, pp. 115\u2013127, 1992.", "Y. Song, \"On the convergence of the MAOR method\", Journal of Computational and Applied Mathematics, vol.79, pp. 299-317,1997.", "M. T. Darvishi, P. Hessari, B.C. Shin, \"Preconditioned modified AOR method for systems of linear equations\", International Journal for Numerical Methods in Biomedical Engineering, vol.27, pp. 758-769, 2011.", "R. S. Varga, Matrix Iterative Analysis, in: Springer Series in Computational Mathematics, vol. 27, Springer-Verlag, Berlin, 2000.", "A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM Press, Philadelphia, 1994."]}

In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.