Breast cancer is a very common and serious cancer for women that is diagnosed in one of every eight Australian women before the age of 85. The conventional method of breast cancer diagnosis is mammography. However, mammography has been reported to have poor diagnostic capability. In this paper we have used subset polynomial neural network techniques in conjunction with fine needle aspiration cytology to undertake this difficult task of predicting breast cancer. The successful findings indicate that adoption of NNs is likely to lead to increased survival of women with breast cancer, improved electronic healthcare, and enhanced quality of life.