To Localize Small Damage from Mode Shapes, the Polynomial Annihilation Edge Detection Method Has Been Proposed and Demonstrated its Effectiveness on Different Types of Structural Components [7]. However, Much Computational Effort Involved in This Approach Lowers the Damage Detection Speed. to Alleviate This Difficulty, in This Paper, We Improve the Approach by First using the Divided Difference Approach to Identify the Region(S) in Which Jump Discontinuities Are Located, and Then Only Applying the Polynomial Annihilation Method to Points in the Identified Region. in This Way, the Computational Burden of This Approach is Significantly Relieved, While the Accuracy is Still Maintained. the Improved Approach Has Been Validated by Numerical Simulations on a Cable-Stayed Bridge Model. This Approach Only Requires Post-Damage Mode Shapes. Copyright © 2013 by Alstom Technologie AG.