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The functional annotation of proteins is one of the most important tasks in the post-genomic era. Although many computational approaches have been developed in recent years to predict protein function, most of these traditional algorithms do not take interrelationships among functional terms into account, such as different GO terms usually coannotate with some common proteins. In this study, we propose a new functional similarity measure in the form of Jaccard coefficient to quantify these interrelationships and also develop a framework for incorporating GO term similarity into protein function prediction process. The experimental results of cross-validation on S. cerevisiae and Homo sapiens data sets demonstrate that our method is able to improve the performance of protein function prediction. In addition, we find that small size terms associated with a few of proteins obtain more benefit than the large size ones when considering functional interrelationships. We also compare our similarity measure with other two widely used measures, and results indicate that when incorporated into function prediction algorithms, our proposed measure is more effective. Experiment results also illustrate that our algorithms outperform two previous competing algorithms, which also take functional interrelationships into account, in prediction accuracy. Finally, we show that our method is robust to annotations in the database which are not complete at present. These results give new insights about the importance of functional interrelationships in protein function prediction.