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Robust high-order matched filter (RHMF), utilizing high-order statistics and considering the inherent variability in target spectral signatures, has obtained better results than other classical detection methods through experiments. However, this algorithm fails to get a fast convergence result by using simple steepest decent. In this paper, we accelerate this algorithm-RHMF successfully by introducing quasi-Newton method and DFP corrector formula, which is a more effective optimization algorithm based on second derivation, into this algorithm. We experiment constrained energy minimization (CEM), adaptive coherence estimator (ACE), RHMF with the steepest descent, and RHMF with quasi-Newton method on real data. The experiment by using RHMF with quasi-Newton has better and faster result, indicating that it is more effective for hyperspectral target detection. We also give the proof of the convergence of this method.