Catalyzes the transformation of cystathionine to homocysteine. Also exhibits cysteine desulfhydrase activity in vitro, producing sulfide from cysteine. H2O + L,L-cystathionine = L-homocysteine + NH4(+) + pyruvate an S-substituted L-cysteine + H2O = a thiol + NH4(+) + pyruvate Amino-acid biosynthesis; L-methionine biosynthesis via de novo pathway; L-homocysteine from L-cystathionine: step 1/1. Constitutively expressed at a low level. No visible phenotype. Belongs to the class-II pyridoxal-phosphate-dependent aminotransferase family. MalY/PatB cystathionine beta-lyase subfamily.