Djay66 from iPhone-Privacy has jailbroken iOS 4.3 on iPhone 4. He has released pwnage Tools for this. Pwnage tools provide semi-tethered jailbreak on iOS 4.3b1 for iPhone4.

For this process, you need to create your own ramdisk to be able to restore. It’s advisable to boot tethered with “tetheredboot” to enjoy unsigned apps.

Steps to follow
1. Download the Ramdisk Maker from http://www.iphone-privacy.com/ramdisk_maker.zip.
2. Open ramdisk.sh with any text editor.
3. Change tools path and your user directory name in TO CHANGE section.
4. Open Terminal.
5. Type “su root” and your password.
6. Type “/path/to/./ramdisk_maker.sh” and follow the instructions.

NOTE: Don’t run Cydia when you have booted untethered as it will crash MobileSafari and some other apps too.