Classical pitch-based perturbation measures, such as Jitter and Shimmer, are generally based on detection algorithms of pitch marks which assume the existence of a periodic pitch pattern and/or rely on the linear source-filter speech model. While these assumptions can hold for normal speech, they are generally not valid for pathological speech. The latter can indeed present strong aperiodicity, nonlinearity and turbulence/noise. Recently, we introduced on a novel nonlinear algorithm for Glottal Closure Instants (GCI) detection which has the strong advantage of not making such assumptions. In this paper, we use this new algorithm to compute standard pitch-based perturbation measures and compare its performances to the widely used tool PRAAT. We address the task of classification between normal and pathological speech, and carry out the experiments using the popular MEEI database. The results show that our algorithm leads to significantly higher classification accuracy than PRAAT. Moreover, some important statistical features become significantly discriminative, while they are meaningless when using PRAAT (in the sense that they have almost no discrimination power).