Intercepted signal blind separation is a research topic with high importance for both military and civilian communication systems. A blind separation method for space-time block code (STBC) systems is proposed by using the ordinary independent component analysis (ICA). This method cannot work when specific complex modulations are employed since the assumption of mutual independence cannot be satisfied. The analysis shows that source signals, which are group-wise independent and use multi-dimensional ICA (MICA) instead of ordinary ICA, can be applied in this case. Utilizing the block-diagonal structure of the cumulant matrices, the JADE algorithm is generalized to the multidimensional case to separate the received data into mutually independent groups. Compared with ordinary ICA algorithms, the proposed method does not introduce additional ambiguities. Simulations show that the proposed method overcomes the drawback and achieves a better performance without utilizing coding information than channel estimation based algorithms.