  Fintushel-Stern's knot surgery gave many pairs of exotic manifolds, which are
homeomorphic but non-diffeomorphic. We show that if an elliptic fibration has
two parallel, oppositely oriented vanishing circles (for example $S^2\times
S^2$ or Matsumoto's $S^4$), then the knot surgery gives rise to standard
manifolds. The diffeomorphism can give an alternative proof that Scharlemann's
manifold is standard (originally by Akbulut [Ak1]).
