Cousins can marry in Japan. This is legal matter. Not cultural.
To Anton
"the degree of relationship" is level of distance between relatives.
Parents and children are level 1.
Brothers and sisters are level 2.
So in case of cousin, it's level 4 because cousin is like "father's(level 1) brother's(level 2) daughter(level1)."
We simply add all levels between you and the person in question, to find what the level of distance is.
And we can't marry a relative up to level 3.