One of the most common methods of contrast enhancement is Histogram Equalization (HE). But it has problems of over-enhancement owing to its global nature and the mean of output brightness does not correlate with the input. Quantile based HE combats both these problems by applying histogram equalization on local sub-histograms. Due to dynamic scaling of the intensity probability distribution, the average brightness of the output correlates with the input image, and at the same time, improves AMBE and MSSI, but falls short in maximising PSNR. As per the current scenario, LQSWDHE has improved upon the short comings of normal Histogram Equalization and has shown better results than competing algorithms. But the algorithm, when simulated for values of Q (number of values), PSNR value appears to decrease, which is undesirable. Therefore the scope of this paper is to propose an improvement to LQSWDHE so as to improve the PSNR value while maintaining the AMBE and MSSI parameters, as they indicate how similar the output is to the input. This has been achieved by the proposed algorithm by introducing a Brightness Preserving Bi-Histogram Equalization block before the original histogram equalization step in the algorithm. © 2019 IEEE.