  We show a method to construct a special Lagrangian submanifold L' from a
given special Lagrangian submanifold L in a Calabi-Yau manifold with the use of
generalized perpendicular symmetries. We use moment maps of the actions of Lie
groups, which are not necessarily abelian. By our method, we construct some
non-trivial examples in the cotangent bundles of the spheres which are non-flat
Calabi-Yau manifolds equipped with the Stenzel metrics.
