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Though mathematical morphology can process the binary and grayscale image successfully, this theory can not extend to the color image directly. Since the vectorial ordering must be applied for color image, marginal ordering (M-ordering) can easily be considered to color morphology. However, M-ordering can produce new color vectors. In this paper, a new approach is proposed, which also orders vectorial components along each dimension independently, but can not produce any new color artifacts. By this new approach, when each component are merged to form the color pixel, if this color pixel is not a new color, it can be final output pixel; but if this is a new color, the final output color should be computed based on the result of each component. Furthermore, two applications of the proposed approach are present, and the results are also discussed.