This paper introduces a novel approach for complex cepstrum analysis. Given initial estimates of complex cepstra and respective instants of glottal closure, the method iteratively optimizes the complex cepstrum and instants of glottal closure so that the mean squared error between natural and reconstructed speech waveforms is minimized. The proposed approach results in a more accurate speech representation based on the complex cepstrum, with no need of windowing or phase unwrapping. Experimental results show that the proposed method produces reconstructed speech with higher segmental signal-to-noise ratio scores when compared with conventional methods of complex cepstrum analysis. Because this approach can derive the complex cepstrum at fixed periods, it can be applied to statistical modeling in parametric speech synthesizers.