A general iterative method of restoring linearly degraded images [R. J. Mammone and R. J. Rothacker, J. Opt. Soc. Am. A4(1), 208-215 (1987)] has been reformulated into a more tractable fixed point iterative procedure. The new formulation is an implementation of the steepest descent algorithm. The slow convergence of the original method is found to be due to its inherent step size. A new method is presented whose increased step size offers accelerated convergence. The realization of the accelerated method is shown to require only a minor modification of the original algorithm. A new stopping criterion is also introduced. Computer simulations demonstrate a significant improvement in the rate of convergence of the new method.