This paper presents a Lyapunov stability theory based adaptive filter algorithm with a determined step size. The proposed algorithm thanks to its step size leads to a faster convergence rate and a lover misadjustment error in case of the noisy measurement environments. Also the proposed algorithm ensures to estimate the best optimal unknown weight vector by using a step size. Simulations on white and non-white Gaussian input signals justify the proposed algorithm for the noisy environments. The simulation results demonstrate good tracking capability and low misalignment error of the proposed algorithm in case of the noisy measurement environments for system identification problems.