Color image enhancement is a technique which makes an image more vivid for human vision. Most affecting color elements for the image are intensity, contrast and saturation. In handling these color elements with the conventional coordinates, their geometric form is important in view of valid gamut. Of them, IHS coordinate appropriately represents human color perception and it is easy to manipulate hue, intensity and saturation of the image. The geometric form of this coordinate is, however, nonlinear, so that it is difficult to control the element values since they may exceed the valid gamut. In this paper, a modified IHS coordinate system is proposed to remedy the nonlinearity of IHS system. The proposed coordinate is derived to linearize the relationship between the saturation and intensity. To improve the image quality, contrast is increased by maximizing the dynamic range of intensity, and saturation is normalized in full range of the intensity because the ratio between the changed saturation values should be maintained the same ratio as between original values. Hue is preserved to keep the characteristic property of the color image. This coordinate system is easy to enhance color images and avoid the gamut-overflow problem.