This note investigates the stability of switched Boolean networks (SBNs) under arbitrary switching signal by using the tool of semi-tensor product of matrices. First, an algebraic expression is given for the SBN via the semi-tensor product. Based on it, a necessary and sufficient condition is presented for the switching point reachability of the system. Second, using the switching point reachability, the pointwise stabilizability is studied, and a necessary and sufficient condition is obtained. Finally, the global stability of SBNs under arbitrary switching signal is investigated, and an easily verifiable necessary and sufficient condition is presented. Two illustrative examples are presented to show that the main results are effective in analyzing the stability of SBNs.