How do I jailbreak iPhone 4 with iOS 4.2.1

Run TinyUmbrella tool and save all SHSHs.
If you have baseband 1.59.00, you need to protect it from getting updated. Run TSS server (in TinyUmbrella).
Restore 4.2.1 normally in iTunes.
iTunes will stop with error 1013 or 1015. This means the baseband was not updated and is desired.
Download and install the latest greenpois0n.
Put your device into DFU mode and run greenpois0n.
Activate your iPhone in iTunes with an original SIM card.
Restore data and sync in iTunes if desired.
Install Cydia with the new Loader on your Springboard or, if it doesn't work, with redsn0w.

last edit: 2011-02-07

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