The soft-input-soft-output (SISO) MSK demodulator is a key component in the iterative receiver for coded MSK systems. To reduce the complexity of the optimal SISO MSK demodulator using the BCJR algorithm, a low complexity suboptimal MSK demodulator was developed by K. R. Narayanan et al. However, our investigation on the symmetric information rate of MSK with the suboptimal demodulator shows that it incurs a significant information rate loss compared with the BCJR demodulator. To avoid the rate loss, a low complexity SISO MSK demodulator is derived based on a new factor graph for MSK, which is found to have comparable complexity to the suboptimal demodulator. Moreover, the proposed algorithm is equivalent to the BCJR algorithm and thus achieves optimal performance. Simulation results for LDPC coded MSK systems are provided to demonstrate the effectiveness of the proposed algorithm. © 2014 IEEE.