Exact histogram specification (EHS) transforms the histogram of an input image into the specified histogram. In the conventional EHS techniques, the pixels are first sorted according to their graylevels, and the pixels that have the same graylevel are further differentiated according to the local average of the pixel values and the edge strength. The strictly ordered pixels are then mapped to the desired histogram. However, since the conventional sorting method is inherently dependent on the initial graylevel-based sorting, the contrast enhancement capability of the conventional EHS algorithms is restricted. We propose a modified EHS algorithm considering the just noticeable difference. In the proposed algorithm, the edge pixels are pre-processed such that the output edge pixels obtained by the modified EHS can result in the local contrast enhancement. Moreover, we introduce a new sorting method for the pixels that have the same graylevel. Experimental results show that the proposed algorithm provides better image enhancement performance compared to the conventional EHS algorithms.