  We consider the defocusing, $\dot{H}^1$-critical Hartree equation for the
radial data in all dimensions $(n\geq 5)$. We show the global well-posedness
and scattering results in the energy space. The new ingredient in this paper is
that we first take advantage of the term $\displaystyle - \int_{I}\int_{|x|\leq
A|I|^{1/2}}|u|^{2}\Delta \Big(\frac{1}{|x|}\Big)dxdt$ in the localized Morawetz
identity to rule out the possibility of energy concentration, instead of the
classical Morawetz estimate dependent of the nonlinearity.
