It also allegedly features Boko Haram leader Abubakar Shekau, a man Nigeria's military twice has claimed to kill in 2009 and again last year. Two weeks ago the military said they had killed in battle a Shekau lookalike who had posed in the group's videos.
"Here I am, alive and I will remain alive until the day Allah takes away my breath," the man says in the Hausa language. "Even if you kill me ... It will not stop us imposing Islamic rule ... We are still in our Islamic state, reigning and teaching the Koran."
The video was made available to The Associated Press through the same channels used previously and seems to show the same man claiming to be Shekau.
In the latest video, he says they are prosecuting in accordance with Shariah law in areas under their control.
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Examples of punishments are shown, including the stoning death of a man apparently accused of adultery, the amputation of the hand of a young man accused of theft, the lashings of a man and what appears to be a girl covered in the hijab.
Two pilots and an Alpha jet have been missing since Sept. 11 when it left the northeastern town of Yola on a bombing mission against Boko Haram.
The video shows a kneeling man in a camouflage vest with his right hand in a sling, with a fighter hovering over him with an axe, which is later used in the beheading.
Speaking in English, the victim identifies himself as a wing commander in the Nigerian Air Force and says he was undertaking a mission in Kauri area of northeast Borno state on September 11.
Nigeria's Defense Headquarters has denied speculation that Boko Haram brought down a helicopter gunship that crashed in August. The pilot died, two crew members survived.