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In this paper, we investigate Borel exceptional values of meromorphic solutions of Painlevé III difference equations. In particular, let w be a transcendental meromorphic solution of w¯w̲(w−1)=η(w−λ) with finite order, where η (≠0), λ (≠0,1) are constants. If a, b are two Borel exceptional values of w, then a+b=1+η and ab=λ=η2.