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This work addresses the problem of improving the convergence and the accuracy of a Bussgang blind equalization scheme, by imposing a set of linear constraints to the equalizer coefficients. As indicated in [G. Jacovitti et al. (2001)], these constraints are obtained exploiting a property of second order statistics (SOS) of the fractionally sampled received signal. While in [G. Jacovitti et al. (2001)] an estimation of the channel autocorrelation is needed, here we obtain a different set of linear constraints without any preliminary channel autocorrelation stage. Numerical results show the improvement of the convergence of the Bussang algorithm that incorporates SOS based constraints, particularly in communications schemes that present high cardinality constellations or small number of available samples.