This paper addresses the issue of dependence between operational losses and how it can be accounted for in the value of capital at risk associated with operational risk. In contrast to the Loss Distribution Approach described by regulators in Basel II, our model accounts for the underlying dependence between aggregate losses of different classes of risk. For the first time in this research area, we model this dependence, assuming that it is driven by both, dependence between loss frequencies and dependence between loss severities. The model implementation shows that values of capital at risk obtained based on the Loss Distribution Approach are different than values obtained using our approach. This finding reveals that accounting for loss dependence in capital at risk computations is important for both banks and regulators. This is because a capital charge against operational losses should reflect true operational risk exposure of a bank. When correctly computed across all banks this w