The paper considers the network of identical oscillators
where , , is a projection matrix that selects the components of that are involved in the coupling. The connection matrix is assumed to satisfy
The main result provides conditions for global complete synchronization of this network, i.e. for all and . These conditions extend the results of the authors in [Physica D 195, No. 1–2, 159–187 (2004; Zbl 1098.82622)] to the case of arbitrary asymmetrical connection matrix .