The effectiveness of the treatment of breast cancer depends on its timely detection. An early step in the diagnosis is the cytological examination of breast material obtained directly from the tumor. This work reports on advances in computer-aided breast cancer diagnosis based on the analysis of cytological images of fine needle biopsies to characterize these biopsies as either benign or malignant. Instead of relying on the accurate segmentation of cell nuclei, the nuclei are estimated by circles using the circular Hough transform. The resulting circles are then filtered to keep only high-quality estimations for further analysis by a support vector machine which classifies detected circles as correct or incorrect on the basis of texture features and the percentage of nuclei pixels according to a nuclei mask obtained using Otsu's thresholding method. A set of 25 features of the nuclei is used in the classification of the biopsies by four different classifiers. The complete diagnostic procedure was tested on 737 microscopic images of fine needle biopsies obtained from patients and achieved 98.51% effectiveness. The results presented in this paper demonstrate that a computerized medical diagnosis system based on our method would be effective, providing valuable, accurate diagnostic information.