Anaesthesia is a state of temporary controlled loss of awareness induced for medical purposes. An accurate assessment of the depth of anaesthesia (DoA) has always been required. However, the current DoA algorithms have limitations such as inaccuracy or inflexibility. In this study, for more reliable DoA assessment, pre-denoised electroencephalograph (EEG) signals are divided into ten frequency bands (α, β1, β2, β3, β4, β, βγ, γ, δ and θ), and the basic complexity measure is done by using spectral entropy (SE). SE from beta-gamma frequency band (21.5 - 38.5 Hz) and SE from beta frequency band show the highest R squared value (0.8458 and 0.7312, respectively) with currently the most popular DoA index, bispectral index (BIS). A new DoA index is developed based on these two SE values for monitoring the DoA and evaluated by comparing with the BIS index. The highest Pearson correlation coefficient is 0.918, and the average is 0.80. In addition, the proposed index shows an earlier reaction than BIS index when the patient from deep anaesthesia to moderate anaesthesia, and the consistency in the case of poor signal quality (SQ) while the BIS Index exhibits inflexibility with cases of poor SQ.