In this paper, we consider a soft-input and soft-output iterative bounded-distance decoding (SISO-IBDD) algorithm in which the bounded-distance decodings are performed sequentially. And we study a computation method of a soft-output value to approximate Max-Log-MAP. In the decoding algorithm, search centers are generated by the sums of the hard-decision sequence obtained from a received sequence and test patterns which are selected beforehand, and the bounded-distance decodings with respect to the search centers are performed. We have proposed a selection method of test patterns for an iterative bounded-distance decoding (IBDD) algorithm in [5]. Simulation results have shown that the IBDD algorithm whose test patterns are selected by the proposed method with considerably small number of iterations provides better error performance than the Chase II decoding algorithm for several BCH codes over an AWGN channel using BPSK signaling. We adopt the selection method of test patterns for the SISO-IBDD algorithm and a computation method of a soft-output value which is modified based on the proposed method in [2] with respect to reliability factors. Over the AWGN channel using the BPSK signaling, we show bit error rates and average soft-output values given by the SISO-IBDD algorithm for the extended BCH (64, 36, 12) and (64, 45, 8) codes by computer simulation. For the extended BCH codes, the simulation results show that bit error rates of the SISO-IBDD algorithm are relatively smaller than those of a Chase-like decoding algorithm with the same number of iterations of the bounded-distance decodings and for each component bit, average soft-output values provided by the SISO-IBDD algorithm are close to those by the Max-Log-MAP decoding algorithm by computer simulation.