  D.Nash defined a family of homotopy 4-spheres in [11]. Proving that his
manifolds ${\mathcal S}_{m,n,m',n'}$ are all real $S^4$, we find that they have
handle decomposition with no 1-handles, two 2-handles and two 3-handles. The
handle structures give new potential counterexamples of Property 2R conjecture.
