The application of the adaptive filtering techniques in system identification and control has received a great interest to model an unknown plant based on the minimisation of the mean square error criterion. Any physical system is well represented by an auto-regressive moving average transfer function. Hence, the infinite impulse response adaptive filter is able to match a zero-pole transfer function with fewer number of coefficients. In this paper a new adaptation algorithm is introduced to update the forward and the backward filter coefficients. The proposed adaptive filter matches efficiently the unknown systems which are modeled by all pole and zero-pole transfer functions. The filter coefficients have converged exactly to the optimal values.