Chi et al. proposed a fast kurtosis (a fourth-order statistic) maximization algorithm (FKMA) and a turbo source separation algorithm (TSSA) for the estimation of the multiple nonGaussian inputs and identification of an instantaneous multiple-input multiple-output (MIMO) system with a given set of noisy output measurements. In this paper, a nonlinear relation between the instantaneous MIMO system and the source extraction filter for TSSA and that for FKMA are proved which hold true for finite signal-to-noise ratio. Based on these relations, two iterative blind system identification (BSI) algorithms for instantaneous MIMO systems are proposed, which are robust against additive Gaussian noise and perform better than FKMA and TSSA, respectively. Some simulation results are provided to support the efficacy of the proposed two BSI algorithms and their performance comparison with FKMA, TSSA and some existing second-order statistics based algorithms.