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An efficient iterative method is proposed for computing the electromagnetic fields scattered from a one dimensional (1D) flat surface. The new iterative method is based on a similar implementation to the Conjugate Gradient Fast Fourier Transform (CG-FFT), where acceleration of the matrix-vector multiplications is achieved using fast Fourier transforms (FFT). However, the iterative method proposed is not based on Krylov subspace expansions and is shown to converge faster than GMRES-FFT and CGNE-FFT while maintaining the computational complexity and memory usage of those methods. Analysis is presented deriving an explicit convergence criterion.