There is a little program called Wondershare MobileGo. At first I thought it was a false program or a virus, but I gave it the benefit of the doubt and downloaded it anyways. I opened it up, connected a Galaxy S4 i337 and BAM, rooted just like that.
From what I've seen this Wondershare program can root almost anything you throw at it. Not only that but it's a very very very (can't emphasize this enough) useful program that everyone should be using. If you want to know everything it can do then you'll have to install it and test it out yourself and trust me, you won't regret it.
I couldn't even believe it. I would add screenshots but it was so simple... If you don't believe me, I don't really care. It's your loss. Have fun rooting your device with another method.
