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A completely new synthesis method, the successive approximation method, is developed. By introducing a control function and a step-by-step approach program various directivity functions can be obtained in which the peaks of the sidelobes and specified zeros fit within a specified curve. This method is applicable to any form of array. Numerical calculations have been done to illustrate its applications: determining optimum current distribution of linear arrays, unequally spaced arrays, steering the main beam through current excitation, etc.