Chronic sleepiness is a common symptom in the sleep disorders, such as, Obstructive Sleep Apnea, Periodic leg movement syndrome, narcolepsy etc. It affects 5% of the adult population and is associated with significant morbidity and increased risk to individual and society. MSLT and MWT are the existing tests for measuring sleepiness. Sleep Latency (SL) is the main measures of sleepiness computed in these tests. Existing method of SL computation relies on the visual extraction of specific features in multi-channel electrophysiological data (EEG, EOG, and EMG) using the R&K criteria (1968). This process is cumbersome, time consuming, and prone to inter and intra-scorer variability. In this paper we propose a fully automated, objective sleepiness analysis technique based on the single channel of EEG. The method uses a one-dimensional slice of the EEG Bisprectrum representing a nonlinear transformation of the underlying EEG generator to compute a novel index called Sleepiness Index. The SL is then computed from the SI. A strong correlation (r = 0.93, rho = 0.0001) was found between technician scored SL and that computed via SI. The proposed Sleepiness Index can provide an elegant solution to the problems surrounding manual scoring and objective sleepiness.