In this paper we point out some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives of higher order are co-ordinated $s$-convex in the second sense. Our established results generalize the Hermite-Hadamard type inequalities established for co-ordinated $s$-convex functions and refine those results established for differentiable functions whose partial derivatives of higher order are co-ordinated convex proved in recent literature.