The present study analyzes the effect of local pairwise orientation relations on the perception of textural structure. We have employed a new class of stochastic stimuli comprised of paired Gabor patches with a particular orientation difference (theta) and relative angular position (phi). We measured the threshold proportion of signal pairs for discriminating the target texture from a noise texture comprised of randomly oriented pairs. The results showed that observers were sensitive not only to textures containing pairs with curvilinear configurations such as lines and curves (phi = theta / 2), but also to their orthogonal configurations such as V shapes and parallels (phi = theta / 2 + 90). Both classes of configuration exhibit the property of co-circularity, a fundamental geometric feature of edges and contours in natural images. We also found higher sensitivity for textures made from orientation pairs with either large or small orientation differences. These results suggest that in addition to orientation difference, co-circularity plays a critical role in the perception of orientation-based textural structure.