MOTIVATION: Classifying proteins into functional families can improve our understanding of protein function and can allow transferring annotations within one family. For this, functional families need to be 'pure', i.e., contain only proteins with identical function. Functional Families (FunFams) cluster proteins within CATH superfamilies into such groups of proteins sharing function. 11% of all FunFams (22 830 of 203 639) contain EC annotations and of those, 7% (1526 of 22 830) have inconsistent functional annotations. RESULTS: We propose an approach to further cluster FunFams into functionally more consistent sub-families by encoding their sequences through embeddings. These embeddings originate from language models transferring knowledge gained from predicting missing amino acids in a sequence (ProtBERT) and have been further optimized to distinguish between proteins belonging to the same or a different CATH superfamily (PB-Tucker). Using distances between embeddings and DBSCAN to cluster FunFams and identify outliers, doubled the number of pure clusters per FunFam compared to random clustering. Our approach was not limited to FunFams but also succeeded on families created using sequence similarity alone. Complementing EC annotations, we observed similar results for binding annotations. Thus, we expect an increased purity also for other aspects of function. Our results can help generating FunFams; the resulting clusters with improved functional consistency allow more reliable inference of annotations. We expect this approach to succeed equally for any other grouping of proteins by their phenotypes. AVAILABILITY AND IMPLEMENTATION: Code and embeddings are available via GitHub: https://github.com/Rostlab/FunFamsClustering. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.