  In this article we construct a new family of simply connected symplectic
4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to
rational surfaces by using rational blow-down technique. As a corollary, we
conclude that a rational surface ${\mathbf CP}^2 \sharp 7{\bar{{\mathbf
CP}}^2}$ admits an exotic smooth structure.
