I'll assume you already know the risks involved in flashing firmware to your device and are happy to proceed. As always, both myself and AndroidPIT assume no responsibility for any damage that may occur to your device.
1. Download the firmware here: Android 4.3 firmware test Samsung i9505 Galaxy S4.
2. Unzip the zip file, and you will get two files with the extension .tar.md5 and a file with the extension .tar
3. Download Odin 3.09, and unpack the .zip also.
4. Launch Odin.
5. Reboot your Galaxy S4 in download mode (Volume Up + Power + Home button).
6. Connect your Galaxy S4 via USB cable to your computer and wait for Odin to recognize it. A blue box should then appear (in the program).
AP_I9505XXUEMJ3_1840064_REV06_user_low_ship_MULTI_CERT.tar.md5 to the AP box
BL_I9505XXUEMJ3_1840064_REV06_user_low_ship_MULTI_CERT.tar.md5 in the BL box
CP_I9505XXUEMJ3_1840064_REV06_user_low_ship_MULTI_CERT.tar.md5 in the CP box
CSC_OLB_I9505OLBEMJ2_1765174_REV06_user_low_ship_MULTI_CERT.tar.md5 in CCS box
8. Make sure that the re-partition box is not checked.
9. Click Start and wait a few minutes until the procedure ends. Do not disconnect your S4, be patient.
10. Once your Galaxy S4 restarts, it's over!
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