Desynchronization of the alpha rhythm is usually quantified as a loss of power in the alpha band. In this study we describe an alternative approach where desynchronization is characterized as an increase in the irregularity of the EEG signal. A new measure, the acceleration spectrum entropy (ASE), is used to quantify EEG irregularity. The ASE is the normalized information entropy of the amplitude spectrum of the second derivative of a time series. The ASE is a measure of the randomness or irregularity of a time series and ranges from 0 (straight line) to 100 (discrete random signal). The ASE was calculated for short EEG epochs under eyes closed and eyes open conditions in 15 subjects. There was a significant increase in ASE in the eyes open condition, reflecting an increase in EEG complexity. The ASE is a sensitive measure of EEG desynchronization.