Winocm posted a video of an iPhone 4 jailbroken on iOS 7.1.1, and claims that this jailbreak is untethered, and it should work on other devices if you put in the effort.
According to Wincom "Oh yeah, this is iOS 7.1.1 untethered if you didn't notice earlier. (iPhone 4 GSM though, don't want to mess with any other devices that I have. Would work elsewhere... if you put in the effort. ジ)"
The photo is an iPhone 5C running Cydia 1.1.9 on iOS 7.1.1, and while these photos can easily be faked, Esser has released previous jailbreaks so you can assume the photo is legit. He explained "That iOS 7.1.1 jailbreak is not based on a long vulnerability chain. It uses a single beautiful kernel bug that goes from mobile to kernel."