The enzyme, found in vertebrates, has no activity toward alpha-(gamma-L-glutamyl)-L-amino acids (cf. EC 4.3.2.9, gamma-glutamylcyclotransferase). The enzyme acts as a cyclotransferase, cleaving the amide bond via transamidation using the alpha-amine of the gamma-L-glutamyl residue, releasing it as the cyclic 5-oxo-L-proline.