Dude lol Look here about what SSJ4 is...it has been said countless times and well yah.
http://anime.myfavoritegames.com/anime-manga/dragonball-gt-movies/89368-rant-about-super-saiyan-4-a.html
http://anime.myfavoritegames.com/anime-manga/dragonball-gt-movies/89378-what-best-name-ssj4-stage.html
http://anime.myfavoritegames.com/anime-manga/dragonball-gt-movies/89220-fur.html
These threads have been dead for a while so you don't need to post but all of them are discussing the very aspect of SSJ4.
If you don't wanna read I will save you the time with a Quick Summary:
SSJ4 doesn't belong in the actual 'saiyajin' family. It is a branch of the Oozaru transformation. Since the Chain doesn't go SSJ1, SSJ2, SSJ3, SSJ4... you see what I mean?
SSJ: Characterized by hair turning golden, them becoming stronger, eyes turning green, hair spiking u.
SSJ2: Chracterized by Golden Hair, spiking up, getting stronger, and then lightning
SSJ3: Longer Golden hair, spikey lightning
SSJ4: Red Fur, Black hair, wild and crazy, monkey like
This makes no sense, however if you put it into Oozaru
Oozaru: A Monkey, fur, wild
Golden Oozaru: SSJ Oozaru, wild, furry, monkey
SSJ4: Wild, furry, monkey like
Although this may sound wrong...think about it and you'll see it's right. All it takes to acess SSJ4 is to be a saiyajin and to have gone SSJ before. The reasoning makes sense:
1.) All saiyajins can go Oozaru, unless their tails are cut off.
2.) It's unknown, but I am thinking all saiyajins can go SSJ if they meet req.
3.) Golden Oozaru = SSJ Oozaru. The user doesn't need to have SSJ3 power. ( Look at Vegeta )