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Blind parameter estimation of the non-minimum phase (NMP) channel with finite impulse response (FIR) is studied. An efficient and reliable blind estimation algorithm is proposed which is based on the combination of second order statistics (SOS) of the received signal and finite alphabet (FA) property of the transmitted signal. Second order statistics based methods provide efficient estimation of channel zeros from a very small number of samples. But SOS based methods are phase blind. The key idea proposed is to use the FA property of the signals resulting from an inverse filter, in conjunction with SOS, to locate the channel zeros, i.e., the FA property is employed to resolve the ambiguity of the system zero location. The equalizer output signal could be exploited recursively at the receiver to improve the estimation accuracy using the FA property. The superior behavior of the proposed method is demonstrated by simulation examples and comparison with some recent works.