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The paper is concerned with adapted solution of a multi-dimensional BSDE witha "diagonally" quadratic generator, the quadratic part of whose $i$th componentonly depends on the $i$th row of the second unknown variable. Local and globalsolutions are given. In our proofs, it is natural and crucial to apply bothJohn-Nirenberg and reverse H\"older inequalities for BMO martingales.

Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators