  Einstein-Hilbert action with a determinantal invariant has been considered.
The obtained field equation contains the \texttt{inverse Ricci tensor},
$\Re_{\alpha\beta}$. The linearized solution of invariant has been examined,
and constant curvature space-time metric solution of the field equation gives
different curvature constant for each values of $\sigma$. $\sigma=0$ gives a
trivial solution for constant curvature, $R_{0}$.
