How to upgrade a jailbroken 4th gen iPod touch to 5.1 or higher?

I was wondering how I could upgrade my jailbroken iPod touch 4g (4.1) to 5.1 or higher? I found the following instructions by cksum on the forum: > You will require iTunes. Connect the device, then right click on it in > the iTunes side bar. Select "Back Up." Allow it to runs its course. > Close iTunes. > > Then put the device into DFU mode: > > 1) Power off the device. > 2) Disconnect it. > 3) Hold the power button for 2 secs. > 4) Without letting go of the power button, press and hold the home button for 10 secs. > 5) Let go of the power button but not the > home button for another 10 secs. > > Reconnect the device and launch iTunes. It will detect your iPad and > inform you it is in recovery mode. From there, it will check for the > newest available update (5.1), download it and install it. When that > completes, simply restore your device from the backup you made > earlier. But I was just wondering if after this I would have to jailbreak my iPod again.