In this paper, we propose a new multi-group multi-cast beamforming design method for phase shift keying (PSK) modulated signals. Quality of service (QoS)-aware optimization is considered where the aim is to minimize transmission power of multiple-antenna base station under the QoS constraints of single-antenna users. In this paper, we show that symbol-level beamforming scheme proposed in the literature is not an effective design method for multi-group multicasting and modify it using rotated constellation approach in order to reduce transmission power. Proposed method enforces the known interference in a constructive manner such that the received symbol at each user is inside the correct decision region for any set of symbols. Hence, designed beamformers can be utilized throughout a transmission-frame rather than symbol-by-symbol basis. An alternating direction method of multipliers (ADMM) algorithm is presented for the proposed design problem and closed-form update equations are derived for the steps of the ADMM algorithm. Simulation results show that the proposed method decreases the transmission power significantly compared to the conventional and symbol-level beamforming.