This paper proposes a lossless color coordinate transform for lossless color image coding. Lossless color coordinate transforms are used to remove the correlation and to bias the signal energy ratio between the color signal components. In order to form the lossless coding, a ladder network is used. It is confirmed by the numerical simulations that the performance of the lossless coding scheme with the lossless color coordinate transform is better than that without the lossless color coordinate transform.