While emphasizing the intensity or saturation component for getting high-quality color images, keeping the hue component unchanged is important; thus, perceptual color models such as HSI and HSV have been used. Hue-Saturation-Intensity (HSI) is a public color model, and many color applications are commonly based on this model. However, the transformation from the HSI color space to the RGB color space after processing intensity/saturation in the HSI color space usually generates the gamut problem. In this study, we clear the relationship between the RGB gamut and the HSI gamut completely. According to the result, we can check whether the processing result is located inside or outside of the RGB gamut without transforming to the RGB color space. If the processing result is judged outside of the RGB gamut, we apply the effective way of hue preserving correction algorithm which is proposed in this study to the saturation component. Experimental results demonstrate that the proposed algorithm can correct the color distortion caused by the enhancement without reducing the visual effect and it is especially useful for images with rich colors and local high component values.