Iterative decoding of product codes that uses a soft-in/soft-out decoder based on the Chase algorithm. This decoding scheme is quite similar to turbo codes, but makes it possible the implementation of the decoder with low complexity while providing acceptable performance. In this paper, for the product codes composed of extended Hamming codes, we propose a reduction scheme of test patterns in the Chase algorithm, which can reduce the decoding complexity without performance degradation. In addition, we propose a simple, but efficient assignment scheme of artificial extrinsic information to the symbols for which we cannot get reliabilities by the decoding procedure. The simulation results for the proposed schemes are shown and compared with the asymptotic performances that can be calculated by the weight distribution of product codes and the union bound on the BER performances.