A novel method is introduced to synthesize microstrip Nonuniform Transmission Lines (NTLs) for matching between two arbitrary complex frequency dependent impedances in a wideband or multi-band frequency range. First, strip width or the characteristic impedance function of the microstrip NTL is expanded in a truncated Fourier series. Then, the optimum values of the coefficients of the series are obtained through an optimization approach. The usefulness of the proposed method is verified using some examples.