  A knot K in a closed connected orientable 3-manifold M is called a 1-genus
1-bridge knot if (M,K) has a splitting into two pairs of a solid torus V_i
(i=1,2) and a boundary parallel arc in it. The splitting induces a genus two
Heegaard splitting of the exterior of K naturally, i.e., K has an unknotting
tunnel. However the converse is not true in general. Then we study such general
case in this paper. One of the conclusions is that the unknotting tunnel may be
levelled with the torus \partial V_1=\partial V_2.
