Transcriptional repressor with bimodal DNA-binding specificity. Represses transcription in a methyl-CpG-dependent manner. Binds with a higher affinity to methylated CpG dinucleotides in the consensus sequence 5'-CGCG-3' but can also bind to the non-methylated consensus sequence 5'-CTGCNA-3' also known as the consensus kaiso binding site (KBS). Can also bind specifically to a single methyl-CpG pair and can bind hemimethylated DNA but with a lower affinity compared to methylated DNA. Plays a role in postnatal myogenesis, may be involved in the regulation of satellite cells self-renewal (PubMed:27446912). Interacts with HIPK2. Interacts with CBFA2T3. Interacts with ZBTB38. Localizes to chromocenters. Expressed in adult and aged myogenic satellite cells. Not expressed during development, is induced during establishment of satellite cells and acquisition of quiescence. Phosphorylated by HIPK2. This phosphorylation reduces stability and triggers ZBTB4 protein degradation in response to DNA damage. Extended N-terminus.