Background: EEG represents a cost-effective mechanism to evaluate brain function. To realize its potential, it is essential to identify aspects of the signal that provide insight into differences in cognitive, emotional and behavioral outcomes and can therefore aid in diagnostic measurement. Here we define a new metric of the EEG signal that assesses the diversity of waveform shapes in the signal. New method: The metric, which we term waveform complexity, abbreviated as Cw, compares the similarity of the shape of waveforms of long durations by computing the correlation (r) of segments. A distribution of waveform diversity is computed as 1-|r|x100, from which Cw is obtained as the median. Results: We identify the length parameter that provides the maximal variance in Cw across the sample population and therefore greatest potential discriminatory power. We also provide insight into the impact of various manipulations of the signal such as sampling rate, filtering, phase shuffling and signal duration. Finally, as a test of potential application, we demonstrate that when applied to eyes closed EEG recordings in subjects taken immediately prior to taking a Raven's progressive matrix test, this measure had a high correlation to participant's scores. Comparison with existing methods: Cw, while correlated with other similar measures such as spectral entropy, sample entropy and Lempel-Ziv complexity, significantly outperformed these measures in its correlation to participants’ task scores. Conclusions: This waveform complexity measure warrants further investigation as a potential measure of cognitive and other brain states.