This work focuses on the beamforming design for downlink multiple-input single-output (MISO) nonorthogonal multiple access (NOMA) systems. The beamforming vectors are designed by solving a total transmission power minimization (TPM) problem with quality-of-service (QoS) constraints. In order to solve the proposed nonconvex optimization problem, we provide an efficient method using semidefinite relaxation. Moreover, for the first time, we characterize the optimal beam- forming in a closed form with quasi-degradation condition, which is proven to achieve the same performance as dirty- paper coding (DPC). For the special case with two users, we further show that the original nonconvex TPM problem can be equivalently transferred into a convex optimization problem and easily solved via standard optimization tools. In addition, the optimal beamforming is also characterized in a closed form and we show that it achieves the same performance as the DPC. In the simulation, we show that our proposed optimal NOMA beamforming outperforms OMA schemes and can even achieve the same performance as DPC. Our solutions dramatically simplifies the problem of beamforming design in the downlink MISO NOMA systems and improve the system performance.