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This paper proposes a new computational method for retrieving shapes under unpredictable conditions such as when occlusion, geometric distortion, and differences in image resolution occur simultaneously. The human visual system retrieves shapes from incomplete information in the real world, and it has inspired a lot of computational methods of retrieving shapes. In order to retrieve shapes, the observed shapes are decided to be alike or unlike remembered shapes in memory after the comparison of these shapes. To compare the observed and remembered shapes, they must first be appropriately represented so that the points on each shape can be mapped and compared. For this reason, the shape retrieval process needs an appropriate shape representation and shape mapping methods. Moreover, the shape representations should be normalized before the mapping process. However, a normalization process for representations under unpredictable conditions has not yet been established. In this paper, we describe a shape retrieval method that enables us to retrieve shapes under unpredictable conditions with a suitable normalization process. Using curvature partition and angle-length profile, our shape retrieval method normalizes the shape representation before it does the mapping. As a result, unlike the previously proposed methods, it can be used under unpredictable conditions such as when occlusion, geometric distortion, and differences in image resolution occur simultaneously.