Because magnitude-squared coherence function (MSCFs) could lose some phase information, based on the core theorem for the frequency domain coherence in signal processing, called as double spectral theorem, we present the two types of new magnitude coherence functions (MCFs) in order to extract the coherence between two signals and give the conditions that they are equal to 0 or +1 or -1. Here, we further study their properties sensitive to initial phases of two signals and phase difference between two signals. Studying demonstrated that the two type MCFs not only reflect frequency domain coherence of two signals, but also reflect the 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 the phase difference between two signals. We call the properties as their properties sensitive to phase.