The concept of visual cryptography with two completely random shares is applied to color images. In the classic coding the shares are not correlated with the coded image, but are not totally random. We apply a completely random coding, proposed previously for the case of black and white images, to color images. This improves the security of the process. The proposed method has similar properties to those of the majority of purely visual cryptographic methods, including reduced contrast and loss of minor details. In the decoding process no calculations are necessary so the decoding can be done by an unarmed human eye. Using the completely random coding of colors introduces some noise into the results, but its level is moderate. The RGB color model is used and the (2, 2) cryptography scheme is considered.