Recently, a partitioned-block-based frequency-domain Kalman filter (PFKF) has been proposed for acoustic echo cancellation. Compared with the normal frequency-domain Kalman filter, the PFKF utilizes the partitioned-block structure, resulting in both fast convergence and low time-latency. We present an analysis of the steady-state behavior of the PFKF and found that it suffers from a biased steady-state solution when the filter is of deficient length. Accordingly, we propose an effective modification that has the benefit of the guaranteed optimal steady-state behavior. Simulations are conducted to validate the improved performance of the proposed method.