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This paper studies the blind estimation of single-input-single-output channels with finite impulse response (FIR) and nonminimum phase. Based on higher order statistics, we introduce a new algorithm that exploits a matrix pencil constructed from a set of cumulant matrices. By solving a generalized eigenvalue problem, channel estimates (up to a scalar ambiguity) can be obtained from nontrivial generalized eigenvectors of this cumulant matrix pencil. With multiple estimation results available, different schemes are given to extract channel information effectively. The proposed algorithm does not require exact knowledge of the channel length and can function properly under channel length overestimation. Numerical simulations demonstrate the robustness of this new algorithm to various adverse conditions.