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Reverberation degrades the quality of a speech signal within an enclosed space and is undesirable for many multimedia applications. We show that the well-known adaptive blind multichannel identification algorithm employed for speech dereverberation suffers from misconvergence in the presence of bulk delays in the acoustic impulse responses. To address this, we propose to estimate the delay components using the allpass components of the received signals as well as pre-estimating the room impulse responses in the cepstrum domain. These pre-estimates are subsequently used for the initialization of the adaptive algorithm to achieve better impulse response estimates. Our proposed approach addresses the bulk delay problem and improves the convergence performance of the adaptive algorithm for blind system identification.