A general iterative method of restoring linearly degraded images has been introduced recently [J. Opt. Soc. Amer., 4, 208-215 (1987)]. In this paper, the general method is reformulated into a more tractable fixed point iterative procedure. The new formulation is shown to be an implementation of the steepest descent algorithm. The inherent step size of the generalized method is found to be responsible for its slow convergence. A new method is presented whose increased step size offers accelerated convergence. The realization of the new 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.