Catalyzes the peptide bond hydrolysis in Xaa-His dipeptides, displaying the highest activity toward carnosine (beta-alanyl-L- histidine). {ECO:0000269|PubMed:12473676, ECO:0000269|PubMed:1903095, ECO:0000269|PubMed:24891507, ECO:0000269|PubMed:7116644}. This is the function of CNDP1 (carnosine dipeptidase 1, ENSG00000150656).