In this paper we investigate the EigenVector Algorithm for Blind Equalization (EVA), and extend its application to the equalization of time-varying fading channels. The modified iterative algorithm, termed Block-Based EVA (BBEVA), is evaluated in terms of ISI suppression, MSE and by examining the signal constellation at the output of the equalizer. Simulation results show that the BBEVA performs better than the non-blind Least Mean Squares (LMS) algorithm.