In this paper, we propose a novel approach for accurate detection of the vowel onset points (VOPs). VOP is the instant at which the vowel begins in the speech signal. Precise identification of VOPs is important for various speech applications such as speech segmentation and speech rate modification. The existing methods detect the majority of VOPs within 40 ms deviation, and it may not be appropriate for the above speech applications. To address this issue, we proposed a two-stage approach for accurate detection of VOPs. At the first stage, VOPs are detected using continuous wavelet transform coefficients, and the position of the detected VOPs are corrected using the phone boundaries in the second stage. The phone boundaries are detected by the spectral transition measure method. Experiments are done using TIMIT and Bengali speech corpora. Performance of the proposed approach is compared with two standard signal processing based methods. The evaluation results show that the proposed method performs better than the existing methods.