Cytotoxic chymotrypsin-like serine protease with preference for bulky and aromatic residues at the P1 position and acidic residues at the P3' and P4' sites. Probably necessary for target cell lysis in cell-mediated immune responses. Participates in the antiviral response via direct cleavage of several proteins essential for viral replication. {ECO:0000269|PubMed:22156497, ECO:0000269|PubMed:23269243}. This is the function of GZMH (granzyme H, Ensembl gene identifier ENSG00000100450).