In this letter, the higher order terms of the time-harmonic solution due to a point-like horizontal excitation source are investigated. It is found that the surface wave of the r-3/2 order terms polarize in both radial and azimuthal directions, complementing the findings in the literature. At the ground surface, the polarization distribution of this wave demonstrates similar behavior as the magnetic induction lines of a magnetic dipole. It suggests that this wave can be observed near the horizontal excitation source, and thereby its effects need to be taken into account for the application of shallow buried object detection.