As reported earlier, the evad3rs team has released a Cydia package called "evasi0n 6.x Untether" to convert a tethered iOS 6 jailbreak (Redsn0w method) into an untethered solution on any pre-A5 device running iOS 6 (iPhone 4, iPhone 3GS and iPod touch 4G). As iDownloadBlog notes, a user just needs to download the evasi0n package from Cydia stores to transform a tethered jailbreak to untethered variant in a few steps.
Although the conversion method from tethered to untethered solution may come with its own share of untested bugs or flaws, it still helps to retain existing Cydia apps and tweaks (installed over tethered jailbreak) while fiddling with the option of untethered jailbreak. In other words, there is no need to reinstall bulky apps and tweaks just for the sake of using an untethered jailbreak.
NOTE: Users who don't want to risk any issues with conversion method should try restoring to iOS 6.1 using iTunes Backup and Restore option. Then run the regular evasi0n untethered jailbreak solution posted here.
Here is the step-by-step guide to convert iOS 6.x tethered jailbreak into an untethered jailbreak on any pre-A5 device (Courtesy of iPhone Hacks):
Step 1: Launch Cydia and tap on search tab.
Step 2: Search for evasi0n 6.x Untether package.
Step 3: Choose evasi0n 6.x Untether from the search results.
Step 4: Tap the Install button, and then click Confirm button.
Step 5: Once the package is installed, reboot the device.
Step 6: On the first reboot, the evasi0n logo with the status of conversion process like Initiliasing offsets, Cleaning up, Done! Continuing boot etc. appears on the device display.
Step 7: After the second reboot, the device is ready for using Cydia apps over the newly installed evasi0n untethered jailbreak.