Stability properties of the Riccati equation in a recently suggested anti-windup algorithm for recursive parameter estimation are analyzed. Convergence of the resulting dynamic system is implied by that of a linear time-varying difference matrix equation. By means of converging matrix products theory, the linear mapping associated with the system is shown to be a paracontraction with respect to a certain norm. Therefore, measured in that norm, the solution to the matrix equation will not diverge notwithstanding excitation properties of the data. Thus the purpose of anti-windup is achieved.