For power-domain uplink NOMA, a parallelogram-structured constellation design based on minimum distance (MD) criterion has been proposed in . Such design reveals a significant improvement, in comparison with other existing designs, by not only achieving a larger MD, but also outperforming them in both symbol error rates (SER) and achievable transmission rates. In this paper, for the downlink NOMA scenario, a modification of the parallelogram-structured constellation is proposed. Our analysis confirms that the proposed constellation provides a much larger MD than the conventional square constellation design with the MD-maximizing inter-constellation rotation. Furthermore, unlike most of the previous works that assume successive interference cancellation (SIC) receivers, where error propagation and large decoding complexity and latency arise, we adopt the joint maximum-likelihood (JML) detection, together with individual decoding. Simulation results show that by considering the heterogeneous reliability requirements, the proposed constellation design significantly improves the bit error performance of the strong user, while maintains the performance of the weak user. As a result, the proposed scheme is suitable for those applications that require, e.g., low latency, while dictating heterogeneous reliability.