Terahertz (THz) communication is expected to be one of the core enabling technologies for future systems. Due to the poor scattering and severe reflection loss of THz waves, the line-of-sight (LoS) communication is considered as a leading feature in THz multiple-input–multiple-output (MIMO) systems. To realize LoS communication, beam training is a promising scheme to find the beamforming vectors without leveraging explicit channel state information (CSI). In this context, a crucial issue for THz MIMO is how to design the beam codewords for realizing any expected radiation pattern during the training. In particular, the narrow beams can be realized by array response vectors whereas the wide-beam design is still an open problem. In this article, we propose two high-quality algorithms, namely, successive convex approximation (SCA)-based auxiliary target pursuit (SCA-ATP) and the sum of symmetrical array response vectors (S-SARVs), for offline design and real-time design, respectively. Numerical results show that SCA-ATP yields the best performance in terms of the beam-pattern error (BPE) compared with benchmarks, and S-SARV can achieve a close performance to SCA-ATP with low computational complexity.