In this paper, we present a novel depth map enhancement scheme in depth map coding. For this purpose, we develop a coupled shock filter that enhances the coded depth map by the edge sharpening and the noise smoothing. Unlike the previous works that control the edge enhancement by the Gaussian blur or anisotropic diffusion, our approach is different in that the edge sharpening is performed. More specifically, in the first phase, we develop the inflection point in such a way that a pixel belongs to the influence zone of a maximum or a minimum made on the basis of the Laplacian. In the second phase, we suppress the amplified noise while preserving the edge. Two-phase structures allows for the strong slope restoration. Finally, the depth enhancement that performs the new approach is implemented. This results in 6.67% (rendered view) BD-bitrate reduction on average when compared with 3DV AVC-based test model and offers the superior subjective quality in the rendered view.