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The paper proposes a concurrent scheme for blind equalization suitable for high-order QAM signals; this scheme combines Modified Modulus Algorithm (MCMA) and Decision Directed (DD) algorithm. The proposed algorithm makes full use of the advantages of MCMA and DD algorithm and these two algorithms operate concurrently. Furthermore, in such algorithm a novel rule to control the adjustment of DDpsilas tap weights vector is proposed. Simulation with a time-varying Doppler underwater acoustic channel is used to compare the proposed algorithm with the famous Constant Modulus Algorithm (CMA) and MCMA. The simulation results show that besides the capability of compensating the phase offset, the proposed algorithm has faster convergence rate and lower steady state mean square error.