This paper introduces a novel statistical method that can identify relevant time-frequency features in brain signals to distinguish between groups. The feature of interest is the spectrum which characterizes the distribution of a given signal's variance (or power) across frequency oscillations. Brain signals are generally nonstationary in that the distribution of the signals' power across frequency changes over time. The classical Fourier analysis is not formally suitable for time series signals with time-varying spectra. This paper utilizes the SLEX (Smooth Localized Complex EXponentials) basis function to capture the transient features of brain signals. The SLEX basis consists of a set of localized orthogonal Fourier-like waveforms with a built-in mechanism for representing localized spectral features. The best basis is first chosen that maximizes group dissimilarity in the time-varying spectra. However, not all spectral features extracted from the best basis may be useful for discrimination and classification purpose. A thresholding scheme is further developed to remove irrelevant features from the best basis to improve accuracy for classification. In simulations the proposed SLEX-thresholding discriminant method was able to consistently identify the most discriminant time-frequency features and was able to correctly classify signals at a high rate. The method was then applied to magnetoencephalographic data from a standard paired-click paradigm. Discrimination between individuals with schizophrenia and a healthy comparison group confirmed the utility of the method.