The BEKK model is a popular multivariate GARCH processes. The paper develops a new general asymmetric BEKK structure, which is based on recent empirical findings by semi-parametric news impact curves. For estimating the new model, a Markov chain Monte Carlo technique is used. Empirical results for triviarte asset returns from firms in the US indicate that the deviance information criterion favors the new model with a multivariate t distribution, and that co-leverage effects exist among the three assets.