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In this letter, we propose a two-parallel-shape array geometry, consisting of sensors spaced much farther apart than a half-wavelength, to improve estimation accuracy via aperture extension for two-dimensional (2D) direction finding. First, the subarray parallel with the x-axis is employed to extract automatically paired high-variance but unambiguous y-axis direction cosines and low-variance but cyclically ambiguous x-axis direction cosines. Then, the subarray parallel with the y-axis is employed to extract automatically paired unambiguous x-axis direction cosines and cyclically ambiguous y-axis direction cosines. Finally, the high-variance unambiguous direction cosine estimates are used to resolve the low-variance cyclically ambiguous direction cosine estimates to obtain automatically paired azimuth-elevation angle estimates. The propagator method, which requires only linear operations but involves no eigen-decomposition or singular-value decomposition into signal/noise subspaces, is adapted to derive the direction cosines. Therefore, the proposed technique offers high estimation precision with low computational complexity.