  For a compact Riemann surface X of positive genus, the space of sections of
certain theta bundle on moduli of bundles of rank r and level k admits a
natural map to (the dual of) a similar space of sections of rank k and level r
(the strange duality isomorphism). Both sides of the isomorphism carry
projective connections as X varies in a family. We prove that this map is
(projectively) flat.
