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This study presents an improved version of our previously introduced formant tracking algorithm. The algorithm is based on processing the negative derivative of the argument of the chirp-z transform (termed as the differential phase spectrum) of a given speech signal. No modeling is included in the procedure but only peak picking on differential phase spectrum. We discuss the effects of roots of z-transform to differential phase spectrum and the need to ensure that all zeros are at some distance from the circle where chirp-z transform is computed. For that, we include an additional zero-decomposition step in our previously presented algorithm to improve its robustness. The final version of the algorithm is tested for analysis of synthetic speech and real speech signals and compared to two other formant tracking systems.