Many interesting problems of robust stabilization can be solved using the complex function theoretic approach of [1]. This method is based on the construction of a conformal mapping which reduces the original robust stabilization problem to a Nevanlinna-Pick interpolation problem, The main difficulty of this approach lies in the construction the conformal mapping, Here we present a new numerical algorithm to construct such conformal mappings. Then we demonstrate its effectiveness in the synthesis of optimal gain-phase margin controllers.