Turbo decoding is iterative decoding, and the MAP algorithm is optimal in terms of performance in Turbo decoding. The log-MAP algorithm is the MAP executed in the logarithmic domain, so it is also optimal. Both the MAP and the log-MAP algorithm are complicated for implementation. The max-log-MAP algorithm is derived from the log-MAP with approximation, which is simply compared with the log-MAP algorithm but is suboptimal in terms of performance. A modified max-log-MAP algorithm is presented in this paper, based on the Taylor series of logarithm and exponent. Analysis and simulation results show that the modified max-log-MAP algorithm outperforms the max-log-MAP algorithm with almost the same complexity.