In this paper, the concerned CMA (Constant Modulus Algorithm) adaptive equalizer convergence rate and residual inter-symbol interference using cost function in order to improved to the ACMA (Advanced CMA). The CMA method compensates amplitude but does not compensate phase. On the other hand, The RCA (Reduced Constellation Algorithm) method compensates both the amplitude and the phase but it has the convergence rate problem. MCMA method is a way to solve the phase problem of CMA method compensates both the amplitude and the phase after respectively calculating the real and imaginary components. But it is more than poor CMA method in the complexity of hardware and the compensation performance. The cost function can advantages by improving the CMA and a MCMA (Modified CMA) equalizer so that the amplitude and phase retrieval the equalization steady-state to reduce the error by using ISI and faster convergence rate and performance is good SER (Symbol Error Ratio) was confirmed by computer simulations.