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Histogram Equalization (HE) is a very popular algorithm in the field of image enhancement. Its theory is very simple but effective and easy to implement. However, this algorithm can not get good result in some special cases. Furthermore, it will change the mean brightness of original image significantly. According to these drawbacks of HE, some novel algorithms have been proposed. The main target of these algorithms is trying to preserve the brightness and entropy of original image better. But they also decrease the enhancement efforts at the same time. In this paper, a novel algorithm, Normal Matching Histogram Equalization (NMHE), is proposed. Experimental results show that this algorithm can not only preserve the mean brightness and entropy of original image but also keep the enhancement efforts simultaneously.