  Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth
hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we
show the existence of a complete K\"{a}hler metric on $X \setminus D$ whose
scalar curvature is flat away from some divisor if there are positive integers
$l(>n),m$ such that the line bundle $K_{X}^{-l} \otimes L_{X}^{m}$ is very
ample and the ratio $m/l$ is sufficiently small.
