Conventional parametric stereo (PS) audio coding employs inter-channel phase difference and overall phase difference as phase parameters. In this article, it is shown that those parameters cannot correctly represent the phase relationship between the stereo channels when inter-channel correlation (ICC) is less than one, which is common in practical situations. To solve this problem, we introduce new phase parameters, channel phase differences (CPDs), defined as the phase differences between the mono downmix and the stereo channels. Since CPDs have a descriptive relationship with ICC as well as inter-channel intensity difference, they are more relevant to represent the phase difference between the channels in practical situations. We also propose methods of synthesizing CPDs at the decoder. Through computer simulations and subjective listening tests, it is confirmed that the proposed methods produce significantly lower phase errors than conventional PS, and it can noticeably improve sound quality for stereo inputs with low ICCs.