In the phase I part of the study the MTD of BKM120 when combined with bevacizumab was determined to be 60 mg/day. In the Phase II part of this study, patients with relapsed/refractory GBM following first line therapy are being treated with the BKM120/bevacizumab combination. Limited BKM120 pharmacokinetic evaluation will be performed on all patients treated during this part of the study. Patients will be reevaluated for response to treatment after 2 cycles (8 weeks). Patients with objective response or stable disease will continue treatment, with subsequent reevaluations every 8 weeks, until disease progression or unacceptable toxicity occurs.