Pitolisant (BF2.649) in the Treatment of Excessive Daytime Sleepiness in Patients With Obstructive Sleep Apnoea Syndrome, Treated or Not by Nasal Continuous Positive Airway Pressure, But Still Complaining of Excessive Daytime Sleepiness

Inclusion Criteria: * Male and/or female outpatients aged from at least 18 years. * Patients complaining of EDS refusing to be treated by nCPAP therapy or having been submitted to nCPAP therapy for a minimum period of 3 months, and still complaining of EDS despite the efforts made beforehand to obtain an efficient nCPAP therapy. * Polysomnography performed (for patients submitted to nCPAP therapy - under nCPAP) between V1 and V2 or during the last 12 months with Apnea-Hypopnea Index (AHI): for patients without nCPAP therapy ≥ 15; for patients under nCPAP therapy less or equal to 10. * For patients submitted to nCPAP therapy: nCPAP ≥ 4 hours / day (compliance checked on the clock-time counter of the CPAP machine) * Mini Mental State Examination (MMSE) ≥ 28 * Beck Depression Inventory - 13 items (BDI-13) score \< 16 and item G (suicidal ideation) of BDI-13 = 0 * Body Mass Index (BMI) less or equal to 40 kg/m² * Epworth Sleepiness Scale (ESS) ≥ 12 * Female patients with child-bearing potential using a medically accepted method of birth control (i.e. oral contraceptives of normal average dosage) agreeing to continue this method throughout the study, and during the month following treatment discontinuation, being negative to serum pregnancy test performed at the screening visit. * If specified by the investigator, the patient must be willing not to operate a car (if sleepy at wheel) or heavy machinery for the duration of the trial or as long as the investigator deems it clinically indicated. In addition, the patient should be willing to maintain during the study their usual behaviors which could affect their diurnal sleepiness (e.g. circadian rhythm, caffeine consumption, nocturnal sleep duration) * Patients having signed and dated the informed consent form. Exclusion Criteria: * Patients suffering from chronic severe insomnia in accordance with the International Classification of Sleep Disorders (ICSD 2005) without OSA * Patients with co-existing narcolepsy (ICSD 2005), judged on clinical criteria * Patients with sleep debt not due to OSA (according to the physician' s judgment) * Patients with non-respiratory sleep fragmentation (restless leg syndrome…) * Shift work, professional drivers * Refusal from the patient to stop any current therapy for EDS or predictable risk for the patient to stop the therapy * Patients suffering from a psychiatric disease * Acute or chronic disease preventing the improvement assessment, e.g. severe chronic obstructive pulmonary disease (COPD) * Current or recent (within one year) history of drug, alcohol, narcotic or other substance abuse or dependence * Any significant serious abnormality of the cardiovascular system, e.g. recent myocardial infarction, angina, hypertension or dysrhythmias (within the previous 6 months), Electrocardiogram Fridericia corrected QT interval higher than 450 ms, history of left ventricular hypertrophy or mitral valve prolapse * Severe co-morbid medical or biological conditions that may jeopardize study participation at the discretion of the investigator (particularly in the cardiovascular system and the instable diabetes). * Positive serology tests (HIV, HCV and HBsAg) * Pregnant or breast-feeding women. * Women with child-bearing potential and no efficient birth-control method * Patients unable to understand the study protocol. * Patients with suspected or known hypersensitivity to study medication * Patients with a dominant arm deficiency impeding the achievement of the tests * Patients using a prohibited medication. * Congenital galactose poisoning, glucose and galactose malabsorption, deficit in lactase. * Patients participating in another study or being in a follow-up period for another study.