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The sixth generation networks envision the deployment of terahertz (THz) band as one of the key enabling property thanks to its abundant bandwidth. However, the ultra-wide bandwidth in THz causes beam-split phenomenon due to the use of a single analog beamformer (AB). Specifically, beam-split makes different subcarriers to observe distinct directions since the same AB is adopted for all subcarriers. Previous works mostly employ additional hardware components, e.g., time-delayer networks to mitigate beam-split by realizing virtual subcarrier-dependent ABs. This paper introduces an efficient and unified approach, called beam-split-aware (BSA) hybrid beamforming. In particular, instead of virtually generating subcarrier-dependent ABs, a single AB is used and the effect of beam-split is computed and passed into the digital beamformers, which are subcarrier-dependent while maximizing spectral efficiency. Hence, the proposed BSA approach effectively mitigates the impact of beam-split and it can be applied to any hybrid beamforming architecture. Manifold optimization and orthogonal matching pursuit techniques are considered for the evaluation of the proposed approach in multi-user scenario. Numerical simulations show that significant performance improvement can be achieved as compared to the conventional techniques.