Recently, the normalized subband adaptive filter (NSAF) algorithm has attracted much attention for handling colored input signals. Based on the first-order Markov model of the optimal weight vector, this paper provides some insights for the convergence of the standard NSAF. Following these insights, both the step size and the regularization parameter in the NSAF are jointly optimized by minimizing the mean-square deviation. The resulting joint-optimization step size and regularization parameter algorithm achieves a good tradeoff between fast convergence rate and low steady-state error. Simulation results in the context of acoustic echo cancelation demonstrate good features of the proposed algorithm.