  We proved the color reflection relation, U(1)-decoupling, Kleiss-Kuijf and
Bern-Carrasco-Johansson relation for color-ordered $\mathcal{N}=4$ Super
Yang-Mills theory using $\mathcal{N}=4$ SYM version BCFW recursion relation,
which depends only on the general properties of super-amplitudes. This verified
the conjectured matter fields BCJ relation. We also show that color reflection
relation and U(1)-decoupling relation are special cases of KK relation, if we
consider the KK relation as a general relation, then the former two relations
come out naturally as the special cases.
