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Turbo product codes (TPC) are very suitable for applications requiring a large code length, a high code-rate, and good error performance. In the Chase decoding algorithm, normally a few least reliable positions are selected and the test sequences are generated from these positions. This paper proposes two methods to lower the complexity of the Chase-Pyndiah decoding algorithm. The first scheme reduces the number of least reliable positions by excluding those having relatively low error probabilities. The other one minimizes computations on unnecessary positions in an algebraic decoder. With these methods, we can significantly reduce the number of test sequences and lower the number of utilized positions for constructing an extended candidate codeword set. We show the simulation results with a squared (64, 57, 4) extended Hamming code-based TPC.