The push towards low-power and wearable sleep systems requires using minimum number of recording channels to enhance battery life, keep processing load small and be more comfortable for the user. Since most sleep stages can be identified using EEG traces, enormous power savings could be achieved by using a single channel of EEG. However, detection of REM sleep from one channel EEG is challenging due to its electroencephalographic similarities with N1 and Wake stages. In this paper we investigate a novel feature in sleep EEG that demonstrates high discriminatory ability for detecting REM phases. We then use this feature, that is based on spectral edge frequency (SEF) in the 8–16 Hz frequency band, together with the absolute power and the relative power of the signal, to develop a simple REM detection algorithm. We evaluate the performance of this proposed algorithm with overnight single channel EEG recordings of 5 training and 15 independent test subjects. Our algorithm achieved sensitivity of 83%, specificity of 89% and selectivity of 61% on a test database consisting of 2221 REM epochs. It also achieved sensitivity and selectivity of 81 and 75% on PhysioNet Sleep-EDF database consisting of 8 subjects. These results demonstrate that SEF can be a useful feature for automatic detection of REM stages of sleep from a single channel EEG.