Chromatin modifications, such as post-translational modification of histone proteins and incorporation of histone variants, play an important role in regulating gene expression. Joint analyses of multiple histone modification maps are starting to reveal combinatorial patterns of modifications that are associated with functional DNA elements, providing support to the 'histone code' hypothesis. However, due to the lack of analytical methods, only a small number of chromatin modification patterns have been discovered so far. Here, we introduce a scalable subspace clustering algorithm, coherent and shifted bicluster identification (CoSBI), to exhaustively identify the set of combinatorial modification patterns across a given epigenome. Performance comparisons demonstrate that CoSBI can generate biclusters with higher intra-cluster coherency and biological relevance. We apply our algorithm to a compendium of 39 genome-wide chromatin modification maps in human CD4(+) T cells. We identify 843 combinatorial patterns that recur at >0.1% of the genome. A total of 19 chromatin modifications are observed in the combinatorial patterns, 10 of which occur in more than half of the patterns. We also identify combinatorial modification signatures for eight classes of functional DNA elements. Application of CoSBI to epigenome maps of different cells and developmental stages will aid in understanding how chromatin structure helps regulate gene expression.