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We show that any depth 2 subfactor with a simple first relative commutant hasa unitary orthonormal basis. As a pleasant consequence, we produce new elementsin the set of Popa's relative dimension of projections for such subfactors. Wealso construct infinitely many new elements in the set of relative dimension ofprojections for subfactors arising from complex Hadamard matrices andbi-unitary matrices.

On Pimsner-Popa orthonormal basis and Popa's relative dimension of projections