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Thalassemia is a genetic defect that is commonly found in many parts of the world. Number of humans that are suffering from this disease is determined by screening the heterozygous population. This article investigates the thalassemia screening problem using the unconstrained functional networks classifier. The learning algorithm for this new scheme is briefly illustrated. The new intelligent system with only sets of second order linearly independent polynomial functions to approximate the neuron functions is tested using thalassemia screening database. The performance of the new approach is compared with the performance of both multilayer perceptron and support vector machines. The results show that this new framework classifier is reliable, flexible, and outperform the most common existing classifiers.