No need downgrade!!
In 4.3 sw first:
1.flash i9505 unlock file with odin, select file in phone section!!!(remove md5 ,flash tar file)
2.type *#0808# select dm+modem+adb and connect phone, wait drivers installed
3.select samsung usb serial port in z3x, and do unlock or repair!!work both option
4.and its very important!after do this job,flash the phone latest sw!!(or only modem file in phone section)
Download and flash patch via Odin Put it on PDA
PATCH FILE - I9505_4.3
Download Here I9505_4.3
Extract after download and add .tar file extention
Password= InfoNec
Select correct phone uart settings in phone
Use Micro UART c3303K cable
Then Direct unlock or Read Code