Inter-color correlation between the luminance component and chrominance components has been utilized for color image coding for years. However, the correlation has not been clearly analyzed. In this paper, we analyze the inter-color correlation and answer two questions related to color image coding: (1) what kind of inter-color correlation exists in color images after the discrete wavelet transform9; and, (2) how strong is it? This analysis helps us to find a most suitable inter-color context and eventually leads to a new embedded color image codec. By using the discovered inter-color context significant performance improvement can be achieved when encoding chrominance components.