  Let $K_1, K_2$ be two knots with $t(K_1)+t(K_2)>2$ and $t(K_1 # K_2)=2$.
Then, in the present paper, we will show that any genus three Heegaard
splittings of $E(K_1 # K_2)$ is strongly irreducible and that $E(K_1 # K_2)$
has at most four genus three Heegaard splittings up to homeomorphism. Moreover,
we will give a complete classification of those four genus three Heegaard
splittings and show unknotting tunnel systems of knots $K_1 # K_2$
corresponding to those Heegaard splittings.
