The Flight Towards the Blue Sky Arc (蒼空への飛翔, Aozora e no Hisyō) is the fourth story arc of the Accel World series. The arc shows Haruyuki and Takumu deal with Seiji Noumi and the truth of Chiyu's sudden betrayal. It explains the mystery of players not appearing on the matching list, as well as introduces the Acceleration Research Society as an antagonistic force. This arc spans the whole fourth novel of the Accel World series. The anime begins the arc in episode 20 and ends in episode 24.
|No.||Title||Japanese Airdate||English Airdate|
|20||Domination (Shihai 支配)||August 24, 2012||August 31, 2013|
|21||Insurrection (Hangyaku 反逆)||August 31, 2012||September 7, 2013|
|22||Determination (Ketsui 決意)||September 7, 2012||September 14, 2013|
|23||Consolidation (Renketsu 連結)||September 14, 2012||September 21, 2013|
|24||Reincarnation (Saisei 再生)||September 21, 2012||September 28, 2013|