Conjoined data is data in which the classes abut but do not overlap. It is difficult to determine the boundary between the classes, as there are no inherent clusters. As a result traditional classification methods, such as Counter-Propagation networks, may underperform. This paper describes a modified Counter-Propagation network that is able to refine the boundary definition and so perform better when classifying conjoined data. The efficiency with which network resources are used suggests that it is worthy of consideration for classifying all kinds of data, not just conjoined data.