Blind signal separation is known as a powerful tool for enhancing noisy speech in many real world environments. In this paper, it is demonstrated that the performance of blind signal separation can be further improved by combining with a null beamformer (NBF). Cascading the blind source separation with null beamforming is equivalent to the decomposition of the received signals into the direct parts and reverberant parts. Investigation of beam patterns of the null beamformer and blind signal separation reveals that directional null of NBF reduces mainly direct parts of the unwanted signals whereas blind signal separation reduces reverberant parts. Further, it is shown that the decomposition of received signals can be exploited to solve the local stability problem. Therefore, faster and improved separation can be obtained by removing the direct parts first by null beamforming. Simulation results using real office recordings confirm the expectation.