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Jigsaw puzzles consist of reconstructing a picture that has been divided into many interlocking pieces. This paper describes an automatic global method for solving the square-piece jigsaw puzzle problem in which neither the orientations nor the locations of the jigsaw pieces are known. This hard combinatorial sorting task is formulated as a nonconvex quadratic programming problem that is solved via the projected power method. Specifically, this work aims to specify the locations and orientations of puzzle pieces by maximizing a constrained quadratic function that resolves an optimized permutation matrix composed of the noisy pairwise affinities between jigsaw pieces. The experimental results obtained in the MIT, McGill and Pomeranz datasets indicate that our method outperforms state-of-the-art techniques.