In this paper, we devise constellations for two-user uplink NOMA systems, that the users accommodate different transmission power levels to the requirements of the present scenario and transmit signals in the same resource block. Existing results employ classical square QAM (SQAM) or its modifications, such as performing an angle rotation, or taking the mutual information into consideration. To provide a better minimum distance (MD) to the joint constellation, which is constructed by superimposing constellations of the two users, we propose a scheme that considers the triangular QAM (TQAM), which is a set of constellation points whose signal points are at the vertexes of contiguous triangles and proved to achieve higher power efficiency than the conventional SQAM. To construct the TQAM-structured joint constellations, the strong user employs a rectangular QAM, while the weak user adopts a TQAM. We derive closed-form expressions for the entire 22m + 22n super-imposed constellation cases with both users adopt constellations with even-power-of-two points. Construction algorithms for both the strong user and the weak user have been provided. Closed-form expressions for the MD are also derived, and the MD analysis shows that the proposed TQAM-structured constellation always attains larger MDs among the existing schemes for NOMA constellation design. Simulation results indicate that the proposed scheme can achieve a promising performance by improving the averaged symbol error rate over other existing schemes.