The speech unit segmentation is an important pre-processing step in the analysis of cleft palate speech. In Mandarin, one syllable is composed of two parts: initial and final. In cleft palate speech, the resonance disorders occur at the finals and the voiced initials, while the articulation disorders occur at the unvoiced initials. Thus, the initials and finals are the minimum speech units, which could reflect the characteristics of cleft palate speech disorders. In this work, an automatic initial/final segmentation method is proposed. It is an important preprocessing step in cleft palate speech signal processing. The tested cleft palate speech utterances are collected from the Cleft Palate Speech Treatment Center in the Hospital of Stomatology, Sichuan University, which has the largest cleft palate patients in China. The cleft palate speech data includes 824 speech segments, and the control samples contain 228 speech segments. The syllables are extracted from the speech utterances firstly. The proposed syllable extraction method avoids the training stage, and achieves a good performance for both voiced and unvoiced speech. Then, the syllables are classified into with "quasi-unvoiced" or with "quasi-voiced" initials. Respective initial/final segmentation methods are proposed to these two types of syllables. Moreover, a two-step segmentation method is proposed. The rough locations of syllable and initial/final boundaries are refined in the second segmentation step, in order to improve the robustness of segmentation accuracy. The experiments show that the initial/final segmentation accuracies for syllables with quasi-unvoiced initials are higher than quasi-voiced initials. For the cleft palate speech, the mean time error is 4.4ms for syllables with quasi-unvoiced initials, and 25.7ms for syllables with quasi-voiced initials, and the correct segmentation accuracy P30 for all the syllables is 91.69%. For the control samples, P30 for all the syllables is 91.24%.