Finally we can find easy solution for tethered boot of jailbroken iPhone downloading iBooty for iOS 6.1.3 and lover firmware versions like iOS 6.1.2, 6.1, 6.0. Usually you can get iBooty 2.3 on your computer only after using latest Sn0wbreeze. But sometimes it absent or not working. I decided to fix this situation offering direct link for 6.1.3 and lower iOS versions.
It is sad to say that there is no untethered jailbreak for iOS 5.1. However there is tethered iOS 5.1 jailbreak which can be performed on your iPhone 4 with Sn0wbreeze 2.9.3. But there is one thing, you have to download and install iBooty 2.3 on your gadget to complete the process.