Along with cognitive and psychobehavioural disorders, gait disorders represent a major problem in the treatment of advanced Parkinson's disease (PD). PD can be considered to be a hyperglutamatergic disease because dopaminergic depletion induces hyperactivity of the subthalamic nucleus (STN) and the internal pallidum (GPi), with glutamatergic hyperactivity of the STN's efferent pathway, i.e., the subthalamopallidal, subthalamonigral and subthalamo-entopeduncular pathways (projecting to the pedunculopontine nucleus (PPN)). Excess glutamate in the PPN has also been observed in the 6-OHDA rat model of PD. Reduction of this glutamatergic hyperactivity within the PPN via the systemic or intra-peduncular administration of glutamate antagonists improves akinesia in drug-induced murine and primate models of PD, via the NMDA and AMPA receptors. High doses of memantine (10 mg/kg) improve locomotion in reserpine- and alpha-methyl-p-tyrosine-treated rats. In humans, the PPN may play a key role in gait, posture control, axial rigidity and attention. It is also involved in the gating of sensory information involved in the startle reflex, which can be studied via prepulse inhibition (PPI) of the blink reflex. At present, two uncompetitive NMDA receptor antagonists are approved for use in humans: amantadine and memantine. Reviews of the recent literature on these drugs have identified no published studies specifically on severe gait and attention disorders in PD. Memantine is a partial blocker of open NMDA channels. The value of memantine relates to the fact that it decreases excessive glutamatergic transmission by lowering the synaptic noise due to excessive activation of NMDA receptors. In this double-blind study, the investigators shall seek to demonstrate the presence or absence of an effect of memantine on gait and attention disorders. In order to study the interaction between glutamatergic hyperactivity and the dopaminergic system, the investigators shall study the phenomena both in the absence of L-dopa and following acute administration of the latter. Twenty eight volunteer, non-demented, late-stage PD patients displaying severe gait disorders will receive memantine (20 mg/day) or placebo for 3 months. The investigators expect to see a reduction in gait and attention disorders, together with an improvement in the blink reflex with PPI under memantine. This pilot study could subsequently be turned into a double-blind, placebo-controlled multicenter study.