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More and more speech technology and signal processing applications make use of the phase information. A proper estimation and representation of the phase goes inextricably along with a correct phase unwrapping, which refers to the problem of finding the instance of the phase function chosen to ensure continuity. This paper proposes a new technique of phase unwrapping which is based on two mathematical considerations: i) a property of the unwrapped phase at Nyquist frequency, ii) the modified Schur-Cohn's algorithm which allows a fast calculation of the root distribution of polynomials with respect to the unit circle. The proposed method is compared to five state-of-the-art phase unwrappers on a large dataset of both synthetic random and real speech signals. By leveraging the two aforementioned considerations, the proposed approach is shown to perform an exact estimation of the unwrapped phase at a reduced computational load.