An aerodynamic design procedure that incorporates the advantages of both traditional response surface methodology (RSM) and neural networks is described. The procedure employs a strategy called parameterbased partitioning of the design space and uses a sequence of response surfaces based on both neural networks and polynomial fits to traverse the design space in search of the optimal solution. This approach results in response surfaces that have both the power of neural networks and the economy of low-order polynomials (in terms of number of simulations needed and network training requirements). Such an approach can handle design problems with many more parameters than would be possible using neural networks alone. The design procedure has been applied to the "blind" redesign of a turbine airfoil from a modern jet engine. This redesign involved the use of 15 design variables. The results obtained are closer to the target design than those obtained using an earlier method with only three design variables. The capability of the method in transforming generic shapes, such as simple curved plates, into optimal airfoils is also demonstrated.