Predicting the function of a protein from its sequence is a long-standing goal of bioinformatic research. While sequence similarity is the most popular tool used for this purpose, sequence motifs may also subserve this goal. Here we develop a motif-based method consisting of applying an unsupervised motif extraction algorithm (MEX) to all enzyme sequences, and filtering the results by the four-level classification hierarchy of the Enzyme Commission (EC). The resulting motifs serve as specific peptides (SPs), appearing on single branches of the EC. In contrast to previous motif-based methods, the new method does not require any preprocessing by multiple sequence alignment, nor does it rely on over-representation of motifs within EC branches. The SPs obtained comprise on average 8.4 +/- 4.5 amino acids, and specify the functions of 93% of all enzymes, which is much higher than the coverage of 63% provided by ProSite motifs. The SP classification thus compares favorably with previous function annotation methods and successfully demonstrates an added value in extreme cases where sequence similarity fails. Interestingly, SPs cover most of the annotated active and binding site amino acids, and occur in active-site neighboring 3-D pockets in a highly statistically significant manner. The latter are assumed to have strong biological relevance to the activity of the enzyme. Further filtering of SPs by biological functional annotations results in reduced small subsets of SPs that possess very large enzyme coverage. Overall, SPs both form a very useful tool for enzyme functional classification and bear responsibility for the catalytic biological function carried out by enzymes.