  We study the supercurrent in a superconductor-ferromagnet-superconductor
heterostructure containing a noncollinear magnetic domain in the ferromagnetic
region. It is demonstrated that the magnetic domain can lead to a spin-flip
process, which can reverse the spin orientations of the singlet Cooper pair
propagating through the magnetic domain region. If the ferromagnetic layers on
both sides of magnetic domain have the same features, the long-range proximity
effect will take place. That is because the singlet Cooper pair will create an
exact phase-cancellation effect and gets an additional $\pi$ phase shift as it
passes through the entire ferromagnetic region. Then the equal spin triplet
pair only exists in the magnetic domain region and can not diffuse into the
other two ferromagnetic layers. So the supercurrent mostly arises from the
singlet Cooper pairs and the equal spin triplet pairs are not involved. This
behavior is quite distinct from the common knowledge that long-range
supercurrent induced by inhomogeneous ferromagnetism stems from the equal spin
triplet pairs. The result we presented here provides a new way for generating
the long-range supercurrent.
