An untethered jailbreak known as ‘UnthreadedJB’ has been released for the CDMA iPhone 4 running iOS 5.1. Prior to this, no program supported an untethered jailbreak for iOS 5.1 (absinthe required 5.1.1 and redsn0w was tethered only).
The team behind the jailbreak has no real name other than ‘UnthreadedJB‘; however, the jailbreak has been confirmed working by a various people across the web. Currently it is available for linux only.
It’s believed that the jailbreak uses previous exploits released by established members of the jailbreak community; however, no real information about its workings have been revealed yet.
Also there is test video for UnthreadedJB To Jailbreak ios 5.x.x using fedora – check Video