Complex sentence: Reagan states that it is the only such martial arts system "accredited by the International Society of Black Belts", an organisation that does not exist outside of the promotional literature for Reagan's American Indian Fighting Arts Association.
Split into simpler sentences: Reagan states that it is the only such martial arts system "accredited by the International Society of Black Belts". The International Society of Black Belts does not exist outside of the promotional literature for Reagan's American Indian Fighting Arts Association.