We investigate by angle-resolved photoemission the electronic structure of in situ grown tetragonal CuO, a synthetic quasi-two-dimensional edge-sharing cuprate. We show that, in spite of the very different nature of the copper oxide layers, with twice as many Cu in the CuO layers of tetragonal CuO as compared to the CuO(2) layers of the high-T(c) cuprates, the low-energy electronic excitations are surprisingly similar, with a Zhang-Rice singlet dispersing on weakly coupled cupratelike sublattices. This system should thus be considered as a member of the high-T(c) cuprate family, with, however, interesting differences due to the intralayer coupling between the cupratelike sublattices.