The author is grateful to Les Lander for pointing out an error in the stability section of (1). In fact Theorems 5 and 7 are incorrect. Recently Arkeryd proved a stability theorem for the infinite-dimensional case in the context of the imperfect bifurcation theory of Golubitsky and Schaeffer(3). In his result finitely many derivatives are controlled, the number depending on the codimension of the singularity unfolded. In this note we shall present a stability theorem involving the determinacy of the singularity. The context is the parameter-free potential case, that is, catastrophe theory. The proof is without recourse to the finite-dimensional results, and the theorem concludes an account of a part of singularity theory in Banach spaces, in which the author has tried to use as little as possible of the finite-dimensional theory (1, 2).