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Antenna array design using orthogonal modes has been extensively studied in the past. The design procedure is based on the projection of an arbitrary array factor on a basis defined by a set of orthogonal modes on the array structure. A design method is presented that relies on the construction of an orthogonal basis using the Gram-Schmidt orthonormalization method. Moreover, simplifications of the orthogonal projection are provided reducing the computational complexity of the design procedure. Finally, the validity of the method is displayed with a design example.