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. 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 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.