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A novel two-step algorithm is proposed for blind identification (BID) of a discrete-time K-input P-output (P ≥ K and P > 1) finite impulse response system F(z) = (F1(z), ...,FK (z)) driven by K stationary nonGaussian inputs which are spatially independent but temporally colored. With each input modelled as a moving-average process with model Bk(z), Chi et al.'s (2003) BID algorithm using higher-order statistics based inverse filter criteria is utilized to estimate the combined system H(z) = (F1(z)B1(z),...,FK(z)BK(Z)) in the first step. In the second step, Qiu et al.'s (1997) greatest common divisor computation method is employed to obtain Fk(z) and Bk(z) from the estimated H(z). Some simulation results are presented to support the efficacy of the proposed 2-step BID algorithm.