How To Downgrade iOS 6.1.3 To iOS 6.1 or 6.1.2

For so many people who have upgraded their devices to the latest iOS 6.1.3 and have lost their untethered jailbreak in the process, this tutorial is to help you downgrade back to iOS 6.1.2  or any iOS 6.x

This tutorial is only supported for iPhone 4, iPod 4G and iPhone 3GS with already saved SHSH blobs on the computer. It is not sometimes advisable to use remote fetching of SHSH blobs files from Cydia because it is not reliable.

Needed iTems:

1. iOS 6.x IPSW & 6.0 IPSW
2. Snowbreeze latest version
3. iTunes 11
4. Redsn0w 0.9.15b3
5. Local SHSH blobs for your iOS 6.1.2

Supported device

1. iPhone 4 and 3GS
2. iPod Touch 4G 

Note: As of this writing untethered jailbreak is not working on iOS 6.x if you downgraded from iOS 6.1.3 to 6.x

Procedures

1. Run Snowbreeze. Click on okay at the first prompt and then click the blue arrow at the right bottom of the window
2. Click on Browse for an IPSW. A menu will pop up, select iOS 6.x you have downloaded
3. Snowbreeze will identify your IPSW. click the blue forward arrow again
4. Select iFaith mode and then browse the shsh. folder to select the SHSH for your IPSW
5. Once selected, Snowbreeze will further accept it and then click on Build IPSW
   
   
   
     
   
6. Snowbreeze will build a new IPSW and it will be on the Desktop.
7. Click Ok and Put your device in DFU mode and then launch iTunes
8. When iTunes is launched, it will see a device that needs to be restores. Hold Shift on your computer and click Restore.
9. Select the new IPSW that snowbreeze built for you and iTunes will restore to that IPSW
10. Once Completed, phone may not boot up. Launch Redsn0w in administrator mode
11. Click Extras, the select IPSW. Select IPSW 6.0 and then go back
12. Click Just boot, put device in DFU mode again. Once in DFU mode, Redsn0w will begin the process tethered jailbreak. Check Install Cydia if presented with the menu and then Redsn0w will continue with its works. device will boot up
13. Once completed you will be in iOS 6.x jailbroken. Go to Cydia and then download the Evasi0n untethered package.

Although converting to untethered  with Cydia untethered packcage doesn't seem to work, you can give it a try.
 
I hope this helps someone achieve that downgrade and untethered jailbreak on iOS 6.1.2. Feel free to drop your comments if you encounter problems in the process and I will help resolve it.