Kingo Root does. I used it on my Canadian model, which is an i377m btw, i377 is US model. Just download kingo root app, install to pc, attach the usb and click root. Be sure to allow any pop ups on device, and do NOT allow it to use the cfautoroot method (or odin mode), as that will trip knox. If it gets that far, just close out and run it again. I've had a few handsets take 2 attemps. You can install any custom recovery you want, and run any rom for i377m or international variant of the s4, just keep in mind flashing a custom recovery will trip knox. Kingo root itself, does NOT trip knox, mine is intact. i377m is a candian variant with an unlocked bootloader, i377 is the US version with a locked bootloader. Very different. mentioned due to you saying another method doesn't work on i377. well no, it doesn't, but if you're asking about a Canadian model, it's an i377m, and it will work.
I run 4.3 stock touchwiz, rooted, with wanam to fake official status, nova prime for the kitakat themed stuff.