  Motivated by global applications, we propose a theory of relative endoscopic
data and transfer factors for the symmetric pair $(U(2n),U(n)\times U(n))$ over
a local field. We then formulate the smooth transfer conjecture and fundamental
lemma, establish the existence of smooth transfer for many test functions, and
prove the fundamental lemma for the symmetric pair $(U(4),U(2)\times U(2))$.
