For a given Monge-Ampère manifold $(Y,g_{Y},\nabla_{Y})$ there is a canonically defined dual Monge-Ampère manifold $(Y^{\vee},g_{Y}^{\vee},\nabla_{Y}^{\vee})$ such that $(Y,g_{Y})$ is identified with $(Y^{\vee},g_{Y}^{\vee})$ as Riemannian manifolds, and the local system $(T{Y^{\vee}},\nabla_{Y}^{\vee})$ is naturally isomorphic to the local system dual to $(TY,\nabla_{Y})$ (dual local system is constructed via the metric $g_{Y}$).