This letter introduces the LOOP binary descriptor (local optimal-oriented pattern) that encodes rotation invariance into the main formulation itself. This makes any post processing stage for rotation invariance redundant and improves on both accuracy and time complexity. We consider fine-grained lepidoptera (moth/butterfly) species recognition as the representative problem since it involves repetition of localized patterns and textures that may be exploited for discrimination. We evaluate the performance of LOOP against its predecessors as well as few other popular descriptors. Besides experiments on standard benchmarks, we also introduce a new small image dataset on NZ Lepidoptera. LOOP performs as well or better on all datasets evaluated compared to previous binary descriptors. The new dataset and demo code of the proposed method are available through the lead author's academic webpage and GitHub.