A new multivariate GARCH model called GO-GARCH has been developed to better estimate covariance matrices with more flexibility. This model is an extension of the O-GARCH model and is simpler than the BEKK model. By using unconditional information first, the number of parameters needing estimation is reduced by more than half, making the estimation process more efficient. Both artificial and real-world examples demonstrate the effectiveness of the GO-GARCH model in practice.