The diagnosis of thyroid malignancy by fine needle aspiration (FNA) examination has been proven to show wide variations of sensitivity and specificity. This paper proposes the utilization of a computer-aided diagnosis system based on a supervised classification algorithm from the artificial immune systems to assist the task of thyroid malignancy diagnosis. The core of the proposed algorithm is the so-called BoxCells, which are defined as parallelepipeds in the feature space. Properly defined operators act on the BoxCells in order to convert them into individual, elementary classifiers. The proposed algorithm is applied on FNA data from 2016 subjects with verified diagnosis and has exhibited average specificity higher than 99%, 90% sensitivity, and 98.5% accuracy. Furthermore, 24% of the cases that are characterized as "suspicious" by FNA and are histologically proven nonmalignancies have been classified correctly.