Upgrading to 4.1 While Retaining Original Baseband
WARNING:1 proceed on your own risk. Do not attempt if you’ve not saved your SHSH Blobs and may want to downgrade back to 4.0.1 or earlier!
WARNING 2: even if you have saved your SHSH Blobs, proceed on your own risk! Don’t do this if you ABSOLUTELY must rely on the iPhone 4 unlock!
1) Download TinyUmbrella 4.1.6 Latest Version(The Firmware Umbrella)
2) Close iTunes
3) Start TinyUmbrella 4.1.3
3i) Click Save My SHSH again to save a 4.1 SHSH blob
3ii) Make sure iTunes is still closed
4) Start the TTS Server
5) Make SURE TinyUmbrella doesn’t report any errors! (If TU reports ANY errors it may not protect you from a baseband upgrade. In that case do NOT proceed!)
6) Start iTunes and restore to iOS 4.1. (Important: You must restore, not update!)
7) Accept the iOS 4.1 Update.
8 ) Hold your breath and wait for the download to finish.
9) After the update is complete, don’t panic if iTunes shows the following error messages: “The iPhone could not be restored. An unknown error occurred (10044).” and “iTunes has detected an iPhone in recovery mode. You must restore this iPhone before it can be used with iTunes.” Simply press “OK” on each and proceed to the next step.
10) Return to TinyUmbrella and select “kick device out of recovery”.
11) Your iPhone should now restart and be recognized by iTunes. If everything went well your iPhone 4 is now running iOS 4.1 with baseband 01.59.00. Congratulations!
Added a bit more detail hopefully this will be a bit easier to follow , Tiny Umbrella will also work for a 1015 error .
Also added a video tuturial How to Update iPhone 4 to iOS 4.1 Without Upgrading the Baseband and jailbreaking using limera1n