Recently the constrained ICA (cICA) algorithm has been widely applied to many applications. But a crucial problem to the algorithm is how to design a reference signal in advance, which should be closely related to the desired source signal. If the desired source signal is very weak in mixed signals and there is no enough a priori information about it, the reference signal is difficult to design. With some detailed discussions on the cICA algorithm, the paper proposes a second-order statistics based approach to reliably find suitable reference signals for weak temporally correlated source signals. Simulations on synthetic data and real-world data have shown its validity and usefulness. r 2007 Elsevier B.V. All rights reserved.