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Decomposing a complex computational problem into sub-problems, which are computationally simpler to solve individually and which can be combined to produce a solution to the full problem, can efficiently lead to compact and general solutions. Modular neural networks represent one of the ways in which this divide-and-conquer strategy can be implemented. Here we present a co-evolutionary model which is used to design and optimize modular neural networks with task-specific modules. The model consists of two populations. The first population consists of a pool of modules and the second population synthesizes complete systems by drawing elements from the pool of modules. Modules represent a part of the solution, which co-operates with others in the module population to form a complete solution. With the help of two artificial supervised learning tasks created by mixing two sub-tasks we demonstrate that if a particular task decomposition is better in terms of performance on the overall task, it can be evolved using this co-evolutionary model.