In this paper, a method for synthesizing the linear antenna array patterns with broad nulls(BN) at the interference directions is newly presented. Opposit to the conventional methods in which the weights of array elements are optimized for BN control, this method simplifies the control process for multiple BN directions and widths by optimally perturbing the zero positions inherent to Schelkunoff polynomial transformed from the array factor. It is also shown that this method can be easily applicable to the phased array antennas. The proposed scheme is numerically verified by substituting the extracted complex weights into the array factor.