In this work, we introduce a high precision synthesis algorithm to include the extraction of finite frequency and right half plane (RHP) transmission zeros of an impedance function as Brune/Darlington Type-C sections. After each transmission zero extraction, remaining immittance function is corrected using a parametric approach. It is shown that proposed high precision synthesis algorithm can synthesize immittance functions up to 40 reactive elements with accumulated relative error in the order of 10(-1). The high precision synthesis package is integrated with the real frequency techniques to design matching networks over broadbands. Examples are presented to exhibit the usage of the proposed high precision synthesis algorithm.