This case report describes a patient who developed a non-stump bronchopleural fistula (BPF) after a right lower lobectomy for lung cancer. On re-exploration, the bronchial stump was intact but the membranous portion of the bronchus intermedius was necrotic, causing a large fistula. The patient underwent a completion sleeve bilobectomy, removing the remaining middle lobe and performing a sleeve resection of the involved portion of the main bronchus. The upper lobe bronchus was re-anastomosed, and the patient recovered uneventfully with an intact bronchial anastomosis. This novel procedure successfully treated a rare case of non-stump BPF.