A method based on a joint block-inner diagonalization (JBID) of a set of output auto-correlation matrices at different delays is proposed for convolutive blind source separation (BSS).A new triply iterative algorithm (TIA) following the gradient descent idea is developed to minimize a novel least squares cost function named tri-quadratic cost function which is used to express the approximation of joint block-inner diagonalization.The mixing matrix can be estimated and the source signals can be retrieved in only one stage through seeking the minimum point of the tri-quadratic cost function by alternately estimating one of the three independent variables parameter subsets combining with the block Toeplitz structure of mixing matrix and the block-inner diagonalization structure of the source signals correlation matrices being fully utilized.Furthermore

TIA is shown to have global convergence even in the presence of the estimation error of the matrix group.Simulations results illustrate that the proposed one-stage algorithm has good convergence and can retrieve the source signals more accurately than some other classic two-stage time-domain methods.