Although bulk hexagonal phases of layered semiconducting transition metal dichalcogenides (STMD) such as MoS2, WS2, WSe2 and MoSe2 exhibit indirect band gaps, a mono-layer of STMD possesses a direct band gap which could be used in the construction of novel optoelectronic devices, catalysts, sensors and valleytronic components. Unfortunately, the direct band gap only occurs for mono-layered STMD. We have found, using first principles calculations, that by alternating individual layers of different STMD (MoS2, WS2, WSe2 and MoSe2) with particular stackings, it is possible to generate direct band gap bi-layers ranging from 0.79 eV to 1.157 eV. Interestingly, in this direct band gap, electrons and holes are physically separated and localized in different layers. We foresee that the alternation of different STMD would result in the fabrication of materials with unprecedented optical and physico-chemical properties that would need further experimental and theoretical investigations.