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A design procedure for the synthesis of planar arrays is presented. Synthesis takes into account the desired pattern and the constraint on the directivity index. It makes use of the perturbation method in conjunction with the Lagrange multiplier theory. Starting from an initial array we perturb the element positions by employing an iterative technique. In the iteration, by setting the first variation of the Lagrangian (Cost function) equal to zero we derive the perturbed positions. Perturbation is applied simultaneously along two independent variables, (element coordinates x and y). The final position of the elements results from the last iteration where the stopping criteria are met. The choice of the initial array takes into account the number of elements and the reduction need of nonuniformity in the excitation. Our study is used for various initial geometries and the resulting arrays are shown to comply with the desired pattern and the directivity index.