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Multiple color coordinate systems are usually involved in color image applications or systems. Forward and backward transformations are used to switch between color coordinate systems. The out of gamut problem emerges when the color coordinate systems' gamut is different. Conventional approaches, including clipping R, G, B values and clipping luminance value are not ideal as they both produce severe error in the luminance component of the resulting color or reduce the contrast of the resulting image. We propose to clip the saturation value when a vector is out of the gamut of the LHS or YIQ space using the saturation processing equations. We have conducted experiments to compare three different clipping approaches. The experimental results show that the saturation clipping approach outperforms the other two approaches, in the sense that it can keep the luminance value unchanged. In addition, the contrast of the image produced by saturation clipping is much better than those produced by other clipping approaches.