We find an explicit $C^{infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $mathbb{H}^4$, for $0{leq}t{leq}{varepsilon}$ for some number ${varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.