Based on the core theorem of the frequency domain coherence in signal processing, called as double spectral theorem, we presented the two types of new magnitude-squared coherence function (MSCFs) in order to extract the coherence between two signals and gave the conditions that they are equal to 1 or 0. Here, we further studied their properties sensitive to initial phases of two signals and phase difference between two signals. Studying demonstrated that the two type MSCFs not only reflect frequency domain coherence of two signals, but also reflect phase relationship between two signals. One is sensitive to the phase difference between two signals and the other is either sensitive to the initial phases or phase difference between two signals. We call the properties as their properties sensitive to phase.