This paper proposes a new procedure to detect Glottal Closure and Opening Instants (GCIs and GOIs) directly from speech waveforms. The procedure is divided into two successive steps. First a mean-based signal is computed, and intervals where speech events are expected to occur are extracted from it. Secondly, at each interval a precise position of the speech event is assigned by locating a discontinuity in the Linear Prediction residual. The proposed method is compared to the DYPSA algorithm on the CMU ARCTIC database. A significant improvement as well as a better noise robustness are reported. Besides, results of GOI identification accuracy are promising for the glottal source characterization.