2. Download and install Towelroot-v3.apk(this version does not require internet access).
3. Place your phone into "Download Mode" (press and hold the "Home", "Volume Down", and "Power" keys until the phone powers on and displays warning screen, then press "Volume Up" key) and flash the I337_NC1_Stock_Kernel using Odin's PDA slot(AP in Odin v3.09+).
4. Open the Towelroot app from your app drawer and press "Make it Rain" to root your device.
5. Power off then boot into "Download Mode" again and flash the I337_NJ4_Stock_Kernel also in Odin's PDA slot(AP in Odin v3.09+).
6. Install SuperSU to manage root access. Done!
1. Should the NJ4 ota update fail consider flashing back to stock NB1 using either file in this thread: I337UCUFNB1 4.4 Stock Odin Tars, then take the NJ4 ota update. Or, place the I337_NB1_to_NJ4_OTA_Update.zip onto your ext-sdcard and sideload from stock recovery. Once updated to NJ4 continue from Step 2 above.
2. When flashing the kernels the most common cause of an Odin flash failure is a faulty usb port or cable. Please check before reporting a failure!
1. After flashing the NC1 kernel your phone may run a little wonky, e.g. extreme lag, no wifi, etc., and towelroot may not root on the first try. If that happens reboot and try towelroot once again. Once rooted and after flashing the NJ4 kernel your phone will again run like a champ!
2. Neither User Data nor knox warranty flag will be affected by following the above process.
3. For a great Noob FAQ see this Post thanks to @gonenorsk!
Alternative Safestrap Method (Updated 3/29/2015 - Odin no longer required):
1. Place the I337UCUFNJ4_100%_Stock_Rooted_ROM onto your ext-sdcard.
2. From Safestrap recovery press "Backup" and backup your User Data.
3. Once complete, from the main menu press "Wipe" then "Advanced Wipe" and wipe everything but your ext-sdcard.
4. From the main menu press "Install," then select and install the I337UCUFNJ4_100%_Stock_Rooted_ROM.
5. Once complete, press "Restore" and restore your User Data.
6. From the main menu press "Reboot," then "System." Done!
1. The above process will not affect your User Data or knox warranty flag.
2. This process will update your Modem, Non-hlos, System, Kernel, Stock Recovery, and Bootloader to NJ4 (BusyBox is also pre-installed).
3. The User Data "Backup" and "Restore" steps in the above instructions are not mandatory but will greatly reduce your device's set-up time. All currently installed non-system apps and settings will be automatically restored.
@benwaffle for his flashboot script(built into the ROM) allowing the flashing of kernels via Safestrap.