Unstabilized self-amalgamation of a Heegaard splitting

Let M be a compact orientable 3-manifold, M=V∪SW be a Heegaard splitting of M, and F1, F2 be two homeomorphic components of ∂M lying in the minus boundary of W. Let M⁎ be the manifold obtained from M by gluing F1 and F2 together. Then M⁎ has a natural Heegaard splitting called the self-amalgamation of V∪SW. In this paper, we prove that the self-amalgamation of a distance at least 3 Heegaard splitting is unstabilized. There are some examples to show that the lower bound 3 is the best.