Speech is an integral part of the human communication system. Various pathological conditions affect the vocal functions, inducing speech disorders. Acoustic parameters of speech are commonly used for the assessment of speech disorders and for monitoring the progress of the patient over the course of therapy. In the last two decades, signal-processing techniques have been successfully applied in screening speech disorders. In the paper, a novel approach is proposed to classify pathological speech signals using a local discriminant bases (LDB) algorithm and wavelet packet decompositions. The focus of the paper was to demonstrate the significance of identifying the signal subspaces that contribute to the discriminatory characteristics of normal and pathological speech signals in a computationally efficient way. Features were extracted from target subspaces for classification, and time-frequency decomposition was used to eliminate the need for segmentation of the speech signals. The technique was tested with a database of 212 speech signals (51 normal and 161 pathological) using the Daubechies wavelet (db4). Classification accuracies up to 96% were achieved for a two-group classification as normal and pathological speech signals, and 74% was achieved for a four-group classification as male normal, female normal, male pathological and female pathological signals.