In the area of infinite impulse response (IIR) system identification and adaptive filtering the equation error algorithms used for recursive estimation of the plant parameters are well known for their good convergence properties. However, these algorithms give biased parameter estimates in the presence of measurement noise. A new algorithm is proposed on the basis of the least mean square equation error (LMSEE) algorithm, which manages to remedy the bias while retaining the parameter stability. The so-called bias-remedy least mean square equation error (BRLE) algorithm has a simple form. The compatibility of the concept of bias remedy with the stability requirement for the convergence procedure is supported by a practically meaningful theorem. The behavior of the BRLE has been examined extensively in a series of computer simulations.<>