Rapid eye movement sleep (REMS) is characterized by the appearance of fast, desynchronized rhythms in the cortical electroencephalogram (EEG), similar to wakefulness. The low electromyogram (EMG) amplitude during REMS distinguishes it from wakefulness; therefore, recording EMG signal seems to be imperative for discriminating between the two states. The present study evaluated the high frequency components of the EEG signal from mice (80–500 Hz) to support REMS detection during sleep scoring without an EMG signal and found a strong positive correlation between waking and the average power of 80–120 Hz, 120–200 Hz, 200–350 Hz and 350–500 Hz. A highly negative correlation was observed with REMS. Furthermore, our machine learning approach demonstrated that simple EEG time-series features are enough to discriminate REMS from wakefulness with sensitivity of roughly 98 percent and specificity of around 92 percent. Interestingly, assessing only the higher frequency bands (200–350 Hz as well as 350–500 Hz) gives significantly greater predictive power than assessing only the lower end of the EEG frequency spectrum. This paper proposes an approach that can detect subtle changes in REMS reliably, and future unsupervised sleep-scoring approaches could greatly benefit from it.