Aim is to test the primary hypothesis that the combination of L-carnosine with cognitive training will significantly increase the performance of patients with schizophrenia on memory and learning training tasks compared to pairing cognitive training with placebo. The investigators will also test the secondary hypotheses that in the group receiving L-carnosine increased performance is due to a greater learning rate. Carnosine has antioxidant and antiglycating action and is found in food and the human body. The investigator's choice is guided by several considerations but, primarily the evidence that L-carnosine has neuroprotective effects through its antioxidant features. Briefly, the investigators propose that alterations in metabolism in several neurotransmitter systems (particularly glutamate) can both contribute to, and be modified by, oxidative stress, and therefore antioxidant administration could positively affect neurotransmitter role in synaptic plasticity, learning and memory.