We investigated the dependence of the input impedance and radiation characteristics on the connection angle between the DC bias stripline and the center dipole of a terahertz coplanar stripline dipole antenna in a semi-infinite substrate. Three connection angles, namely 0° (typical horizontal connection), 45° (diagonal connection), and 90° (vertical connection), were examined and an overall performance comparison was provided. The antenna with a sufficiently long bias stripline exhibited a traveling-wave behavior with stable impedance variation, regardless of the connection angle between the DC bias stripline and the center dipole. The antenna with diagonal and vertical bias connections performed much better than the typical H-shaped electrode with a horizontal bias connection in terms of radiation characteristics exhibiting flat gain and low frequency cut-off of the radiation efficiency. In addition, the antenna with a diagonal bias connection exhibited a better radiation pattern and more efficient use of a given substrate area than that with a vertical bias connection. The result indicates that in terms of the overall aspect of the terahertz stripline dipole antenna designs on a high-dielectric-constant substrate, the antenna with a diagonal bias connection is the best configuration.