Due to the spectrum shortage and demand for much higher data rates, millimeter (mm)-wave communications have received growing attention for cellular communication systems with beamforming that can overcome the severe propagation loss. For a highly correlated channel where the line-of-sight (LoS) exists with strong non-LoS (NLoS) components, which would be a typical case for mm-wave channels, we generalize a diversity eigenbeamforming method in this paper. For performance comparisons, the statistical eigenvector beamforming method, which is effective when the LoS exists, is considered as both the diversity eigenbeamforming and statistical eigenvector beamforming methods require statistical properties of channels. It is shown that the diversity eigenbeamforming methods outperforms the statistical eigenvector beamforming method when the NLoS component dominates.