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This paper considers a discrete-time multiuser multiple-input single-output (MISO) Gaussian broadcast channel~(BC), in which channel state information (CSI) is available at both the transmitter and the receivers. The flexible and explicit design of a uniquely decomposable constellation group (UDCG) is provided based on pulse amplitude modulation (PAM) and rectangular quadrature amplitude modulation (QAM) constellations. With this, a modulation division (MD) transmission scheme is developed for the MISO BC. The proposed MD scheme enables each receiver to uniquely and efficiently detect their desired signals from the superposition of mutually interfering cochannel signals in the absence of noise. In our design, the optimal transmitter beamforming problem is solved in a closed-form for two-user MISO BC using max-min fairness as a design criterion. Then, for a general case with more than two receivers, we develop a user-grouping-based beamforming scheme, where the grouping method, beamforming vector design and power allocation problems are addressed by using weighted max-min fairness. It is shown that our proposed approach has a lower probability of error compared with the zero-forcing (ZF) method when the Hermitian angle between the two channel vectors is small in a two-user case. In addition, simulation results also reveal that for the general channel model with more than two users, our user-grouping-based scheme significantly outperforms the ZF, time division (TD), minimum mean-square error (MMSE) and signal-to-leakage-and-noise ratio (SLNR) based techniques in moderate and high SNR regimes when the number of users approaches to the number of base station (BS) antennas and it degrades into the ZF scheme when the number of users is far less than the number of BS antennas in Rayleigh fading channels.