Coding of a color image usually happens in the YCbCr space so that the rate-distortion optimization is conducted in this space. Due to the use of a non-unitary matrix in the RGB-to-YCbCr conversion, an optimal coding performance achieved in the YCbCr space does not guarantee an optimal quality in the RGB space, which would impact most display devices that need RGB signals as the inputs. In this paper, we first study the relationship between the coding distortions of the compressed RGB signals and the quantization errors occurred in the coded YCbCr signals. Then, we design a new quantization scheme crossing the RGB and YCbCr spaces to achieve a high-quality color image compression with the YCbCr 4:4:4 format. Although our proposed quantization takes place in the YCbCr space, it aims at reducing the coding distortion in the RGB space as much as possible. Experimental results demonstrate that our proposed method offers a significant quality gain over the existing block-based coding methods for various images.