The equation error formulation in the adaptive IIR filtering provides convergence to a global minimum regardless a local minimum with a large stability margin. However, the equation error formulation suffers from the bias in the coefficient estimates. In this paper, a new algorithm, which does not require a prespecification of the noise variance, is proposed for the equation error formulation. This algorithm is based on the equation error smoothing and provides an unbiased parameter estimate in the presence of white noise. Through simulations, it is demonstrated that the algorithm eliminates the bias in the parameter estimate while retaining good properties of the equation error formulation such as fast convergence speed and the large stability margin.