Terahertz (THz)-band has been envisioned for the sixth generation wireless networks thanks to its ultra-wide bandwidth and very narrow beamwidth. Nevertheless, THz-band transmission faces several unique challenges, one of which is beam-split which occurs due to the usage of subcarrier-independent analog beamformers and causes the generated beams at different subcarriers split, and point to different directions. Unlike the prior works dealing with beam-split by employing additional complex hardware components, e.g., time-delayer networks, a beam-split-aware orthogonal matching pursuit (BSA-OMP) approach is introduced to efficiently estimate the THz channel and beamformer design without any additional hardware. Specifically, we design a BSA dictionary comprised of beam-split-corrected steering vectors which inherently include the effect of beam-split so that the proposed BSA-OMP solution automatically yields the beam-split-corrected physical channel directions. Numerical results demonstrate the superior performance of BSA-OMP approach against the existing state-of-the-art techniques.