Schlindwein, C., Suslin's hypothesis does not imply stationary antichains, Annals of Pure and Applied Logic 64 153–167. Shelah has shown that Suslin's hypothesis does not imply every Aronszajn tree is special. We improve this result by constructing a model of Suslin's hypothesis in which some Aronszajn tree has no antichain whose levels constitute a stationary set. The main point is a new preservation theorem, the proof of which illustrates the usefulness of certain ideas in [8, Section 1].