In this paper, we investigate a new method for extracting useful information from the group delay spectrum of speech. The group delay spectrum is often poorly behaved and noisy. In the literature, various methods have been proposed to address this problem. However, to make the group delay a more tractable function, these methods have typically relied upon some modification of the underlying speech signal. The method proposed in this paper does not require such modifications. To accomplish this, we investigate a new function derived from the group delay spectrum, namely the group delay deviation. We use it for both narrowband analysis and wideband analysis of speech and show that this function exhibits meaningful formant and pitch information.