By combining Kohonen learning and Grossberg learning a new type of mapping neural network is obtained. This counterpropagation network (CPN) functions as a statistically optimal self-programming lookup table. The paper begins with some introductory comments, followed by the definition of the CPN. Then a closed-form formula for the error of the network is developed. The paper concludes with a discussion of CPN variants and comments about CPN convergence and performance. References and a neurocomputing bibliography with a combined total of eighty entries are provided.