From ModMyi - Wiki

This guide assumes you have a "virginized" iPhone on 1.0.2 and would like to upgrade to 1.1.1 in order to unlock/jailbreak it.

Step 1. - iNdependence.

Download (but do NOT run it yet) iNdependence 1.2.5. If you already downloaded the virginizing pack, then you already have it. its included in there.

Make sure your iPhone is connected to the computer, and iTunes is NOT running. Also open Activity Monitor (Applications/Utilities/Activity Monitor) and make sure iTunes Helper is quit - click it and click Force Quit if its active).

Before continuing with the following steps, you should ensure that your iPhone is activated and jailbroken. You can follow the steps in " Part 2 of the "OS X iPhone Unlock Guide" if you do not know how. Be sure to only follow the steps in "Part 2". Afterwards you should return here and continue with the rest of the steps in this guide.

Now open iNdependence. At the bottom it should say its connected to the iPhone with 1.0.2 firmware, activated and jailbroken (Make sure you activate it and install SSH first) . Click the Firmware tab, and hit the Pre 1.1.1 Upgrade button. You should already have the iPhone set to Auto-Lock: Never, and know the iPhone's IP address. If you're not sure how to do that, check the virginizing guide.

Enter your iPhone's IP address, and your root password. Unless you have changed it, it should be dottie. Click OK.

iNdependence will ask you to open iTunes, and make sure it is on the Set Up Your iPhone screen.

Do so now. I just clicked Set up as a new iPhone and didn't have it sync anything, for time's sake, and re-synced all my info after completing this. You can Restore from the backup of: your phone if you'd like, but I didn't since it takes so long to transfer over all your music.

Once this is complete, go back to iNdependence, and hit OK.

iNdependence may display a Host verification failed. message. If so just hit Yes.

Step 2. - iTunes.

All right, now you will see a Success message. Quit iNdependence, and THEN hit OK.

Download the 1.1.1 firmware. Make sure that the package remains a .zip-file (Safari: Uncheck the Options > General > Open ""safe"" files-checkbox or use Firefox)

Then go back into iTunes, and hit option + Update" to chose location of the firmware.

Locate the 1.1.1 firmware, and click OK.

You'll see some status windows...

You should get a message saying Your iPhone has been updated...

Congratulations! You're updated to 1.1.1! Now, do NOT try to sync to iTunes just yet, as you will only have 300 MB of available space - we're not quite done. We next have to get the iPhone prepped for modding, then we can unlock it.