Visual shape recognition in primates depends on a multi-stage pathway running from primary visual cortex (V1) to inferotemporal cortex (IT). The mechanisms by which local shape signals from V1 are transformed into selectivity for abstract object categories in IT are unknown. One approach to this issue is to investigate shape representation at intermediate stages in the pathway, such as area V4. We studied 109 V4 cells that appeared sensitive to complex shape in preliminary tests. To achieve a more complete picture of shape representation in V4, we tested each cell with a set of 366 stimuli, constructed by systematically combining convex and concave boundary elements into closed shapes. Using this large, diverse stimulus set, we found that all the cells in our sample responded to a wide variety of shapes and did not appear to encode any single type of global shape. However, for most cells the shapes evoking strongest responses were characterized by a consistent type of boundary conformation at a specific position within the stimulus. For example, a given cell might be tuned for shapes containing concave curvature at the right, with other parts of the shape having little or no effect on responses. Many cells were tuned for more complex boundary configurations (e.g., a convex angle adjacent to a concave curve). We quantified this kind of shape tuning with Gaussian functions on a curvature x position domain. These tuning functions fit the neural responses much better than tuning functions based on edge or axis orientation. Thus individual V4 cells appear to encode moderately complex boundary information at specific locations within larger shapes. This finding suggests that, at intermediate stages in the V1-IT transformation, complex objects are represented at least partly in terms of the configurations and positions of their contour components.