When transmitting the so-called “texture-plus-depth” video format, texture and depth maps from the same viewpoint exhibit high correlation. Coded bits from one map can then be used as side information to encode the other. In this paper, we propose to use the depth information to divide the corresponding block in texture map into arbitrarily shaped regions (sub-blocks) for separate motion estimation (ME) and motion compensation (MC). We implemented our proposed sub-block motion prediction (MP) method for texture map coding using depth information as a new coding mode (z-mode) in H.264. Nonetheless, in practical experiments one can observe either a misalignment between texture and depth edges, or an aliasing effect at the texture boundaries. To overcome this issue, z-mode offers two MC types: i) non-overlapping MC, and ii) overlapping MC. In the latter case, overlapped sub-blocks after ME are alpha-blended using a properly designed filter. Moreover, the MV of each sub-block in z-mode is predicted using a Laplacian-weighted average of MVs of neighboring blocks of similar depth. Experimental results show that using z-mode, coding performance of the texture map can be improved by up to 0.7dB compared to native H.264 implementation at high bitrate.