Many animals regularly return to particular locations such as hives, nests, wintering grounds or cache sites. This ability clearly implies that animals possess information that allows them to find a route from their current location to their goal. However, the nature of this information is, in many cases, unknown. One particularly important issue is whether this information encodes at least some of the geometric relationships among real-world objects, which would meet a strict definition of a cognitive map(1,2). Are animals sensitive to such geometric relationships? Although there is dear evidence that animals can learn vectors that represent a goal location in terms of absolute distance and direction to a landmark, there is little evidence of any ability to extract abstract geometric rules(3-8). Here we report data demonstrating that the corvid Clark’s nutcracker (Nucifraga columbiana) can learn to find the point halfway between two landmarks that vary in the distance that separates them. This learning is based on a general principle, as the birds correctly find the halfway point when the landmarks are presented with new distances between them. This demonstrates the ability to find a point defined not by the relationship between a goal and a landmark but by the relationship between landmarks. Further experiments demonstrate that there were two distinct processes involved in locating the halfway point, the use of directional bearings to find the (hypothetical) line connecting the landmarks and finding the correct place along that line.