The convolutive blind source separation (BSS) problem has been received much more attentions in recent years. This paper investigates a convolutive BSS algorithm via employing the time-delayed second-order statistics information and exact diagonalization without any a priori knowledge on the mixtures. This decorrelated second-order statistics and its multi-sample delayed copies, which form two positive-definite symmetry matrices, are obtained from whitened mixtures. By using a set of transforms such as Cholesky decomposition and singular value decomposition (SVD) to these two matrices, a unitary matrix is obtained and utilized to diagonalize them exactly. It attributes the estimates of source signals to this matrix. The similarity between the estimated and original signals is quantified by calculating their correlation coefficients (CC). For the mixtures of speech and noise, ItakuraSaito distance (ISD) is applied to measure the intelligibility of estimated speech signals. Better performance of the investigated algorithm is demonstrated in experimental results compared with the previous algorithm.