Although Constant Modulus Algorithm (CMA) is effective to equalize non-minimum phase channels blindly, it suffers from residual intersymbol interference (ISI) and large Mean Square Error (MSE) when applied to higher order constellations (QAM). Methods based on cost function matched to the signal constellation namely alphabet matched algorithm (AMA) were previously reported and proves its superiority on CMA concerning the MSE. Thus dual mode algorithms between CMA and AMA were introduced. A hybrid technique combining CMA and AMA using a cosine square function as a constellation matched error (CME) was lately reported. In this paper two different CME functions are introduced. The MSE of the proposed algorithms are calculated using matlab simulation under multipath fading channels for different signal to noise ratios (SNR) and different levels of QAM constellations. A comparison is established among them. Depicted results show that the choice of the CME function will mainly depend on the number of constellation points.