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Product codes are powerful codes that can be used to correct errors and/or recover erasures. Judging the erasure recovery performance of a product code based on its minimum distance is pessimistic because the code is actually capable of recovering many erasure patterns beyond those with the number of erasures determined by the minimum distance. By analyzing the non-recoverable erasure patterns, this letter develops a tighter upper bound on the post-decoding erasure rate for any binary product code. The analytical derivations are verified through computer simulations using Hamming and single parity check (SPC) product codes.