If M is a quaternionic manifold and P is an S 1-instanton over M, then Joyce constructed a hypercomplex manifold we call(M) over M. These hypercomplex manifolds admit a U (2)-action of a special type permuting the complex structures. We show that up to double covers, all such hypercomplex manifolds arise in this way. Examples, including that of a hypercomplex structure on SU (3), show the necessity of including double covers of(M).