Catalyzes the synthesis of the inhibitory neurotransmitter gamma-aminobutyric acid (GABA) with pyridoxal 5'-phosphate as cofactor. H(+) + L-glutamate = 4-aminobutanoate + CO2 Homodimer. Deficient mice die at birth with cleft palate and apnea and exhibit reduced levels of glutamic acid decarboxylase and gamma-aminobutyric acid in the cerebral cortex. Belongs to the group II decarboxylase family.