We present a new methodology for discriminating genomic symbolic sequences, which combines wavelet analysis and a self-organizing map algorithm. Wavelets are used to extract variation across various scales in the oligonucleotide patterns of a sequence. The variation is quantified by the estimated wavelet variance, which yields a feature vector. Feature vectors obtained from many genomic sequences, possibly of different lengths, are then classified with a nonparametric self-organizing map scheme. When applied to nearly 200 entire mitochondrial DNA sequences, or their fragments, the method predicts species taxonomic group membership very well, and allows the results to be visualized. When only thousands of nucleotides are available, wavelet-based feature vectors of short oligonucleotide patterns are more efficient in discrimination than frequency-based feature vectors of long patterns. This new data analysis strategy could be extended to numeric genomic data. The routines needed to perform the computations are readily available in two packages of software R.