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We propose a novel Histogram Equalization (HE) to improve contrast of images. As most existing HE methods still suffer from over-enhancement caused by a quantum jump, the proposed method focuses on robustness to deal with the problem in various image conditions. To achieve the goal, we adjust the curve shape of the output mapping function by properly combining the curve shape of the null mapping function and that of the normal mapping function from the conventional HE according to the weighting value. Experimental results show that the proposed method well endures difficult conditions and provides moderate image quality.