The maximization of non-Gaussianity is an effective approach to achieve the complex independent component analysis (ICA) problem. However, the traditional complex maximization of non-Gaussianity (CMN) algorithm does not consider the influence of noise. In this letter, a modification of the fixed-point algorithm is proposed for more practical occasions of the complex noisy ICA model. Simulations show that the proposed method demonstrates significantly improved performance over the traditional CMN algorithm in the noisy ICA model when the sample size is sufficient.