Using the approach that we developed recently, we find the critical line of an anisotropic Ising antiferromagnet on two-dimensional square and honeycomb lattices. We extend our previous lemma and conjecture to be useful in the antiferromagnetic system. We find two interesting behaviors: (1) An antiferromagnet is not necessarily most inert at the absolute zero. (2) The field-driven antiferromagnetic phase transition is possible in the honeycomb lattice.