The blind parameter estimation of a non-minimum phase (NMP) channel having a finite impulse response (FIR) is studied. An efficient and reliable blind estimation algorithm is proposed which is based on a combination of second order statistics (SOS) and the kurtosis of the signals. SOS based methods provide efficient estimation of channel zeros from a very small number of samples. As the SOS based methods are phase blind, the kurtosis is used to resolve the ambiguity in system zero locations. It is also shown that the equalizer output could be exploited recursively to improve the estimation accuracy using finite alphabet (FA) properties. It is noted that, as all the available information for blind channel parameter estimation is used, the proposed method can achieve a very high accuracy. Performance of the estimation method is also discussed.