Can I Downgrade iPhone 4 (GSM)?

Downgrade is Currently Not Supported
Apple is currently only signing iOS 7.1.2 for iPhone 4 (GSM). The signing window for iOS 7.1.1 and all earlier releases has closed.
Apple permanently closes the signing window for older releases within 1 to 2 weeks of launching a newer update. Because Apple's servers authenticate each restore online, trying to install any previous iOS build on iPhone 4 (GSM) will immediately fail with iTunes Error 3194.
June 30, 2014
April 22, 2014
March 10, 2014
February 21, 2014
November 15, 2013
October 22, 2013
September 26, 2013
September 18, 2013
Can I downgrade from an iOS Beta on iPhone 4 (GSM)?
Yes. If your iPhone 4 (GSM) is running an iOS Beta, you can always restore back to the latest signed public release using Recovery Mode in Finder (Mac) or iTunes / Apple Devices (Windows).
Can I downgrade to the iOS version iPhone 4 (GSM) originally shipped with?
No. Apple permanently closes the signing window for older releases. Even though iPhone 4 (GSM) originally launched with an earlier version, Apple servers will no longer authenticate that installation.
What can I do if I cannot downgrade iPhone 4 (GSM) but experience battery or performance bugs?
You can perform a clean restore to the latest signed firmware using a computer to eliminate software glitches and corrupted cache, or await the next minor point update from Apple that includes targeted bug fixes.
Can I downgrade iPhone 4 (GSM) if the signing window has closed?
No. Apple servers reject restore verifications for unsigned builds (returning iTunes Error 3194). Unsigned firmware cannot be installed on standard Apple devices.
Will restoring or downgrading iPhone 4 (GSM) erase data?
Yes. Flashing an IPSW firmware file requires a restore that wipes on-device storage. Ensure your personal data is backed up to iCloud before proceeding.