Given a closed orientable surface S of genus g, a complete Heegaard diagram on the surface S is a maximal collection of disjoint, essential, and pairwise non-isotopic simple closed curves. Given a complete Heegaard diagrams on S, there is a natural handlebody structure determined by the diagram. The associated handlebody is obtained by attaching 2-handles along the curves in the diagram and caping off the 3-manifold by 3-balls. Hatcher and Thurston proved in 1979 that any two complete Heegaard diagrams in S are related by two types of elementary moves. The type II move does not change the handlebody structure associated to the diagrams. The aim of the talk is to show that if two complete Heegaard diagrams determine the same handlebody structure, then they are related by a finite sequence of type II moves. The proof of the result is similar to the argument used in showing that any two ideal triangulations of a compact surface with boundary are related by elementary moves.