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The isolated power system in Kinmen Island, Taiwan has already implemented the special protection system (SPS) to prevent various critical contingencies that occurred during the past decade. However, when a severe N-2 contingency occurred on July 26, 2013, the SPS has not properly armed its under-frequency load shedding. After reexamining transient recorded waveforms, it was observed that the system still has sufficient spinning reserve and the coordination between the under-frequency relay and the current SPS was not well considered. In this article, the current SPS is further modified in order to avoid the occurrence of the excessive load shedding under similar N-2 contingencies. Extensive time-domain dynamical simulations are performed first to study the relationship between the amount of the load shedding and frequency deviations under these extreme N-2 contingencies. Based on these simulation results, the remediation scheme of the SPS will be proposed by modifying the existing SPS design logic and the amount of load shedding. More comprehensive input triggered states are proposed for identifying these severe N-2 contingencies. Both simulation verifications under the proposed remedial scheme and actual transient recorded waveforms under a severe contingency after commissioning this remediated SPS are provided to demonstrate the effectiveness of this proposed remediation scheme. [ABSTRACT FROM AUTHOR]