In medical imaging, accurate diagnosis heavily relies on effective image enhancement techniques, particularly for X-ray images. Existing methods often suffer from various challenges such as sacrificing global image characteristics over local image characteristics or vice versa. In this paper, we present a novel approach, called G-CLAHE (Global-Contrast Limited Adaptive Histogram Equalization), which perfectly suits medical imaging with a focus on X-rays. This method adapts from Global Histogram Equalization (GHE) and Contrast Limited Adaptive Histogram Equalization (CLAHE) to take both advantages and avoid weakness to preserve local and global characteristics. Experimental results show that it can significantly improve current state-of-the-art algorithms to effectively address their limitations and enhance the contrast and quality of X-ray images for diagnostic accuracy.