We formulate sigma-model duality transformations in terms of spin connection, This allows one to investigate the symmetry of the string action including higher order alpha' corrections. An important feature of the new duality transformations is a simple homogeneous transformation rule of the spin connection (with torsion) and specifically adjusted transformation of the Yang-Mills field. We find that under certain conditions this duality is a symmetry of the full effective string action in the target space, free of alpha' corrections. We demonstrate how the exact duality generates new fundamental string solutions from supersymmetric string waves.