In this paper, a new model for the ramp-cepstrum of the one-sided autocorrelation function of a noise-free autoregressive moving average (ARMA) signal is presented. The proposed blind identification technique can estimate the parameters of ARMA systems in both noise-free and noisy environments without using the input observations. It is shown that, utilizing the proposed ARMA ramp-cepstrum model in accordance with a residue-based least-squares optimization technique, both AR and MA parameters of ARMA systems can be directly obtained. The proposed method is tested on synthetic ARMA systems of different orders and also on some natural speech signals. Simulation results demonstrate the efficacy of the proposed identification scheme at low to high SNR levels