An amalgamation of a new technique and an old technique is presented in this paper for the purpose of better enhancement of contrast and brightness preservation of low contrast grayscale segmented images. The proposed technique is named as Hyper Geometrically Modified Absolute Mean Bi-Histogram Equalization (HGAMBHE). The basic idea of the proposed method is to segment the histogram of the image based on Hyper Geometric cumulative distribution function (CDF). Then the segmented histogram of the image is divided into two parts based on an average point with respect to Hyper Geometric CDF. A standard value of above applied distributive function is taken for the calculation of absolute modified mean (AMM) and peak signal to noise ratio (PSNR). Based on absolute modified mean value of the histogram, calculations of different parameters to determine the brightness preservation and contrast enhancement are done. This proposed method is found to provide more accurate and realistic results.