  We present a complete and independent off-shell Green's basis of the
dimension 8 operators in the Standard Model effective field theory (SMEFT). We
propose an off-shell amplitude formalism such that this new kind of amplitudes
has a one-to-one correspondence to general operators carrying all kinds of
redundancies. The advantage of such formalism is that all kinds of redundancies
can be formulated explicitly in terms of the off-shell spinors and thus be
removed systematically from the exhaustive list of the general off-shell
amplitudes. Following such procedure, redundant operators can be reduced to the
ones with the only redundancy from the equation of motion kept, the Green's
basis. We find there are (993+1649) independent (on-shell + off-shell)
operators for one generation of fermions and (44807+66197) ones for three
generations at the dimension 8. This systematic method can be applied to obtain
the Green's basis at any mass dimension for general EFTs.
