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A new color image coding technique is proposed in this paper. The technique is based on the efficient grey-scaled wavelet-based image coding, the context adaptive wavelet difference reduction - CAWDR. The coder exploits not only compactness and self-similarities of wavelet transform in each color component, but also the dependency between the color components. The context adaptive arithmetic coder is implemented to the encoded bit stream. The significant coefficient quantizations for all color components are performed before the refinement pass in each bit-plane. This single bit stream of encoded image has embedded property and exact rate control without explicit information. The performance comparison is also presented in the paper. The proposed coder typically has 0.3 - 1 dB higher average PSNR than that of JPEG2000.