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The objective of this work is to develop an automatic method for estimating glottal opening instants (GOIs) using Hilbert envelope (HE). The GOIs are secondary major excitations after glottal closure instants (GCIs) during the production of voiced speech. The HE is defined as the magnitude of complex time function (CTF) of a given signal. The unipolar property of HE is exploited for picking the second largest peak present in a given glottal cycle and hypothesize as glottal opening instant (GOI). The electroglottogram (EGG) / speech signal is first passed through the zero frequency filtering (ZFF) method to extract GCIs. With the help of detected GCIs, the secondary peaks present in the HE of dEGG / residual are hypothesized as GOIs. The hypothesized GOIs are compared with secondary peaks estimated from the dEGG / residual. The GOIs hypothesized by the proposed method show less variance compared to peak picking from dEGG / residual.