Frequency compounding was recently investigated for computer aided classification of masses in ultrasonic B-mode images as benign or malignant. The classification was performed using the normalized parameters of the Nakagami distribution at a single region of interest at the site of the mass. A combination of normalized Nakagami parameters from two different images of a mass was undertaken to improve the performance of classification. Receiver operating characteristic (ROC) analysis showed that such an approach resulted in an area of 0.83 under the ROC curve. The aim of the work described in this paper is to see whether a feature describing the characteristic of the boundary can be extracted and combined with the Nakagami parameter to further improve the performance of classification. The combination of the features has been performed using a weighted summation. Results indicate a 10% improvement in specificity at a sensitivity of 96% after combining the information at the site and at the boundary. Moreover, the technique requires minimal clinical intervention and has a performance that reaches that of the trained radiologist. It is hence suggested that this technique may be utilized in practice to characterize breast masses.