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Blind deconvolution is aimed at recovering an unknown signal that has been distorted in transmission through an unknown channel. In this work we present a new tool for blind equalization, exploiting a statistical independence criterion based on the log-characteristic function (also termed the second generalized characteristic function (SGCF)). More specifically, the criterion is based on the empirical difference between the joint SGCF and the sum of marginal SGCF, evaluated at pre-selected "processing points". We consider the case of a linear, time invariant (over blocks), possibly nonminimum-phase distortive channel. Using a nonlinear (possibly weighted) least-squares (WLS) approach for minimizing the criterion, we propose an iterative batch-processing-type algorithm for updating a finite impulse response (FIR) "channel inversion"-type equalizer. The algorithm's performance is compared in simulation to the performance attained by the Shalvi-Weinstein kurtosis maximization approach, as well as to the optimal performance attainable by an FIR equalizer (assuming a known channel).