  BCJ relation reveals a dual between color structures and kinematic structure
and can be used to reduce the number of independent color-ordered amplitudes at
tree level. Refer to the loop-level in Yang-Mills theory, we investigate the
similar BCJ relation in this paper. Four-point 1-loop example in N = 4 SYM can
hint about the relation of integrands. Five-point example implies that the
general formula can be proven by unitary- cut method. We will then prove a
'general' BCJ relation for 1-loop integrands by D-dimension unitary cut, which
can be regarded as a non-trivial generalization of the (fundamental)BCJ
relation given by Boels and Isermann in [arXiv:1109.5888 [hep-th]] and
[arXiv:1110.4462 [hep-th]].
