Chronic Dev Team has released a jailbreak tool on the Cydia app store for those who have already installed a tethered jailbreak on their iOS 5.0.1 devices. Using this tool, called Corona 5.0.1 Untether will modify your iPhone with the same exploits used in redsn0w. Unlike the redsn0w jailbreak process, Corona requires no computer to untether a jailbroken device.
In order to successfully install Corona, your iOS device must already have a tethered jailbreak installed along with iOS 5.0.1. Do not use Corona if you're using a hybrid iOS 5.0/5.0.1 jailbreak! This requires installing and running redsn0w after a clean restore to stock iOS 5.0.1.
The difference between a tethered and untethered jailbreak means not having to boot up your iPhone connected to a computer. This ensures that your iOS device actually starts up, and that you have access to jailbreak apps and tweaks at all times.
2. Navigate to Sections -> System -> Corona 5.0.1 Untether or use the Search function to find the package.
3. Tap the package name and touch the Install button in the upper right hand corner.
4. If your current configuration is not compatible with Corona you will receive the message "Cannot Comply". Try using redsn0w instead.
5. Touch the Confirm button in the upper right hand corner.
6. When the package is finished installing your iOS 5.0.1 jailbreak will be untethered.
iPad 2 and iPhone 4S users are still waiting for a jailbreak solution. In the meantime, a jailbroken iPad, iPhone 4, iPhone 3GS, iPod touch 3G or iPod touch 4G can be untethered with Corona using the instructions above.