This research uses eigenvalue characteristics of the Karhunen-Loéve Transform of ionosphereic total electron content (TEC) to investigate precursors for 12 earth quakes of Richter magnitude scale M ≥ 5.0 in a local region of latitude 23.00 to 24.00°N and longitude 120.00 to 121.50°E for 1 January 2002 to 31 December 2003. Previous researchers have found that in the 5 days before these earthquakes (i.e., prior to M ≥ 5.0), pre cursors of clear ionospheric anomalies showing sparser total electron content (TEC) were detected through statistical investigation. This was evidenced through two is sues from Liu and his partners in 2001 and 2006. These is sues gave credible evidence of such precursors. The precursor days having clear extreme eigenvalues of the Karhunen-Loéve Transform as the precursors in stead of the sparser ionospheric TEC were also mostly in the 5 days before the 12 earthquakes of greater than M ≥ 5.0. The precursors of Chi-Chi Earth quake (M_w = 7.6) with clear extreme eigenvalues were detected on the 1st, 3rd, and 4th days be fore this earthquake. These results are consistent with the analyses of Liu and his partner's issue in 2001. These findings verify the validity of the Karhunen-Loéve Trans form. To further verify this approach, the Karhunen-Loéve Trans form is applied to an earthquake in Japan. Precursors to the Japan Iwate-Miyagi Nairiku earthquake (M_j = 7.2), with clear extreme eigenvalues are detected on the 1st, 2nd, and 5th days before the earthquake, respectively. However, after detailed analysis, precursors of earthquakes of Richter magnitude scale M < 5 are not easy to identify using extreme eigenvalues because of existence of other ionospheric features not caused by earthquakes.