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This paper proposes an automatic decomposition algorithm for separating skin image into melanin and hemoglobin components. First, skin region is detected from input image. Then, the whole image is divided into several sub regions. After extracting separation vectors from each sub regions, we use proposed method to distinguish the vectors which corresponds to melanin and hemoglobin components, respectively. Based on our validity rules, invalid vectors are discarded and valid vectors are treated as candidate vectors. Finally, we determine the final separation vectors which have minimal deviation from all of the candidate vectors to separate skin image. The separation results demonstrate the validity of our algorithm. Our experiments with lower resolution and poor quality images as input also verify that the proposed algorithm is very robust.