The CMA and MMA blind equalization algorithm has the inevitable large residual error caused by mismatching between the symbol constellation at a steady state after convergence. Stop-and-Go algorithm has a very superior residual error characteristics at a steady state but a relatively slow convergence characteristics. In this paper, we propose a SAG-Flagged MMA as a new adaptive blind equalization algorithm with a Stop-and-Go flag which follows a flagged MMA in update scheme of tap weights as appling the flag obtaining from Stop-and-Go algorithm to MMA. Using computer simulation, it is confirmed that the proposed algorithm has an enhancing performance from the viewpoint of residual ISI, residual error and convergence speed in comparison with MMA and Stop-and-Go algorithm. Algorithm has a new error function using the decided original constellation instead of the reduced constellation. By computer simulation, it is confirmed that the proposed algorithm has the performance superiority in terms of residual ISI and convergence speed compared with the adaptive blind equalization algorithm of CMA family, Constant Modulus Algorithm with Carrier Phase Recovery and Modified CMA(MCMA).