A method of identification of a mixed-phase system (driven by a zero mean non-Gaussian white noise) from its output, by an autoregressive moving-average (ARMA) model is proposed. This is achieved by relating the bispectrum phase and magnitude to the system group delay functions. The method uses only the bispectrum information and it is applicable for MA, AR, or ARMA systems with either mixed-phase poles, mixed-phase zeros, or both. The identification does not involve any solution of a system of equations and is free from the limitations found in many of the existing methods. Its evaluation for different ARMA terms indicates that its performance is good in terms of root-mean-square (which accounts both for bias and variance), since the normalized sum of the sample mean-square error is about 1%.