How to Update iPhone 4 to iOS 4.3.1 with Preserving 01.59.00 Baseband
STEP 1. First you have to download TinyUmbrella.
STEP 2. Now connect your iPhone 4 to the computer via USB and open TinyUmbrella.
STEP 3. Now simply click on “Save SHSH” button.
STEP 4. Now you have to click on “Start TSS Server” button.
STEP 5. Now launch iTunes while the TSS server is running.
STEP 6. Simply hold down the Shift key and click on Restore button.
STEP 7. Now simply select your iPhone 4.3.1 firmware and click on Open button.
STEP 8. Within iTunes, simply click on Restore button to start restoring your iPhone 4.
STEP 9. iTunes will give you Error 1013 during the Restore Process. This indicates that your baseband has been preserved.
STEP 10. Now simply click on Ok button and close iTunes.
STEP 11. Now you have to put your iPhone into DFU mode. For this simply hold down both Home and Power buttond for 10 seconds, then release the Power button but keep holding the Home button for another five seconds.
STEP 12. Now you have to fix Recovery in TinyUmbrella is currently not working. Simply download this standalone .exe file to fix recovery on 4.3.1. Now extract the file and double click on fixrecovery43.exe. A command prompt will open, and the program will go through the process. You will see scrolling text on your iPhone 4 screen during this time.
That’s it. Now your iPhone 4 will be on iOS 4.3.1 with the 1.59.00 baseband. In this way you can update your iPhone 4 to iOS 4.3.1 while preserving 01.59.00 Baseband. Now you can follow the steps posted here to jailbreak your iPhone 4 on iOS 4.3.1 untethered using Redsn0w 0.9.6RC9. [Via]