Morphologic appearance is one of intuitive diagnosis factors of mass lesions in breast imaging, and irregular shape is one of the most frequent appearances for malignant masses. Thus, an effective measure of morphological irregularity will provide a helpful reference to determine malignancy of breast masses. In this paper, a new measure based on Fourier Transform, named Fourier Irregularity Index (FII), was developed to provide a reliable malignant/benign classification factor. The experiment was conducted with 418 breast masses, including 190 malignant cases and 218 benign cases. Performance was assessed and compared among various methods using Receiver Operating Characteristics (ROC) analysis. The proposed measure in this study achieved malignant/benign classification accuracy of 96% with an area (Az) of 0.99 under the receiver operating characteristics (ROC) curve, which outperformed typical traditional approaches, such as Compactness (accuracy of 90%, Az = 0.96), Fractal Dimension (accuracy of 90%, Az = 0.95), Fourier Factor (accuracy of 90%, Az = 0.97), and Fractional Concavity (accuracy of 75%, A z = 0.65).