So as it turned out, the Verizon iPhone 4 is vulnerable to Limera1n bootrom based exploit, and untethered GreenPois0n kernel based exploit which makes it possible to jailbreak on iOS 4.2.6, untethered using GreenPois0n RC5.4.
The following instructions will help you jailbreak your CDMA based iPhone 4 untethered on Verizon using the latest version of GreenPois0n.
Step 2: Connect your Verizon CDMA iPhone 4 via USB to your computer and click on “Jailbreak” as seen in the screenshot below.
Step 4: GreenPois0n will now start “Jailbreaking” your iPhone, untethered on 4.2.6.
Step 5: Your iPhone should now be successfully jailbroken on iOS 4.2.6. Now start “Loader” found on the homescreen and install Cydia.
Note: The video embedded above was shot when GreenPois0n RC5 was first released. The procedure shown in the video is exactly same for jailbreaking Verizon iPhone 4.