Investigating the electronic structures of the single-layer and heterobilayer of dichalcogenides MoSe₂ and WSe₂ we observe an unusual nature of their excitations. To do so, we used first-principles methods based on density-functional theory (DFT) [1,2] and many-body perturbation theory (MBPT - the GW approximation and the Bethe-Salpeter equation) [3,4] . The specific properties of the subunits, which play the role of building blocks in this van der Waals heterostructures are basically preserved. For example, the semiconducting character of the monolayers is maintained in the heterostructure and only the nature of the band gap was changed. Indeed, our calculations show clearly that the building blocks are direct semiconductor at K point of the Brillouin zone in the visible range while the heterostructure shows type -II band alignment with an indirect gap. Our results open up perspectives to create new low-dimensional materials with customized characteristics.