  The Ward identity in gauge theory constrains the behavior of the amplitudes.
We discuss the Ward identity for amplitudes with a pair of shifted lines with
complex momenta. This will induce a recursion relation identical to BCFW
recursion relations at the finite poles of the complexified amplitudes.
Furthermore, according to the Ward identity, it is also possible to transform
the boundary term into a simple form, which can be obtained by a new recursion
relation. For the amplitude with one off-shell line in pure Yang-Mills theory,
we find this technique is effective for obtaining the amplitude even when there
are boundary contributions.
