  We construct a duality manifest gravitational theory for the special linear
group, ${\mathbf{SL}(N)}$ with $N{\neq 4}$. The spacetime is formally extended,
to have the dimension $\textstyle{\frac{1}{2}} N(N-1)$, yet is `gauged'.
Consequently the theory is subject to a section condition. We introduce a
semi-covariant derivative and a semi-covariant `Riemann' curvature, both of
which can be completely covariantized after symmetrizing or contracting the
${\mathbf{SL}(N)}$ vector indices properly. Fully covariant scalar and `Ricci'
curvatures then constitute the action and the `Einstein' equation of motion.
For $N\geq 5$, the section condition admits duality inequivalent two solutions,
one $(N-1)$-dimensional and the other three-dimensional. In each case, the
theory can describe not only Riemannian but also non-Riemannian backgrounds.
