<p>When using the continuous wavelet transform (CWT), wavelet coefficients in higher scales cannot detect damages and singularities in the structural signal; this is a weakness of CWT. This paper introduces a greedy wavelet transform (GWT), an enhanced version of the one-dimensional continuous wavelet transform, for improved damage localization. In this method, first, the CWT wavelet transform is applied to the damaged structural signal. Then the standard deviation of each scale is calculated from the wavelet coefficients to obtain the standard deviation vector of the wavelet coefficients. A Greedy algorithm finds the scale corresponding to the optimal wavelet coefficients with the lowest standard deviation, so that in the next step, these optimal wavelet coefficients are re-entered into the CWT. This process is iterated until the desired solution is obtained. Experimental validation on a polyurethane sandwich beam under various damage scenarios and mode shapes, using modal analysis for signal acquisition, demonstrates the GWT’s effectiveness in damage detection. The GWT consistently outperforms the conventional wavelet transform across all tested mode shapes and damage scenarios.</p>