Abstract: In this paper step-by-step method is developed further and non-extremum step-by-step method is proposed, It can be applied to whole fit between directivity function and expected function. This method expands applied extent of step-by-step method, therefore, a complete synthesis theory has been constructed. In this paper non-symmetric amplitude shading of linear arrays is also studied. The fit extent between directivity function and expected function can be improved obviously by using this kind of shading.