We show that which that for a Berwald structure, any Riemannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if (M, F ) is a Finsler structure such that there exists a Riemannian structure that leaves invariant the indicatrix under parallel transport of the associated Levi-Civita connection, then the structure (M, F ) is Berwald. As application, a necessary condition for pure Landsberg spaces is formulated. Using this criterion we provide an strategy to solve the existence or not of pure Landsberg surfaces.3 email@example.com Partially supported during the writing of this note by EPRSC and Cockcroft Institute 2 firstname.lastname@example.org. F.E is partially supported by Project MTM2008-01386/MTM (Spain).