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Quaternary structures of proteins are closely relevant to gene regulation, signal transduction, and many other biological functions of proteins. In the current study, a new method based on protein-conserved motif composition in block format for feature extraction is proposed, which is termed block composition. Furthermore, the quaternary structure attribute prediction system which combines block with functional domain composition, called QuaBingo, is constructed by three layers of classifiers that can identify monomer, homo-, and hetero-oligomer quaternary structures. The building of the first layer classifier uses SVM based on blocks and functional domains of proteins, and, the second layer SVM was utilized to process the outputs of the first layer. Finally, the result is determined by the random forest of the third layer. We compared the effectiveness of the combination of block composition, functional domain composition, and pseudo amino acid composition of the model. In the 11 kinds of functional protein families, QuaBingo is 23% of MCC higher than the existing prediction system. The results also revealed the biological characterization of the top five block compositions. QuaBingo provides more accurate predictive ability for protein quaternary prediction.