  Secondary homological stability is a recently discovered stability pattern
for the homology of a sequence of spaces exhibiting homological stability in a
range where homological stability does not hold. We prove secondary homological
stability for the homology of the unordered configuration spaces of a connected
manifold. The main difficulty is the case that the manifold is closed because
there are no obvious maps inducing stability and the homology eventually is
periodic instead of stable. We resolve this issue by constructing a new
chain-level stabilization map for configuration spaces.
