We propose a stable algorithm for blind source separation (BSS) combining multistage ICA (MSICA) and linear prediction. The MSICA in which frequency-domain ICA (FDICA) for a rough separation is followed by time-domain ICA (TDICA) to remove residual crosstalk. For temporally correlated signals, we must use TDICA with a nonholonomic constraint to avoid the decorrelation effect from the holonomic ...