Hypercube multi-computers system is of good performance in parallel and distributed computation. With the increasing size of a multi-computers system, the fault possibility of computers and their links increases. It is very important to seek for better fault-tolerant routing strategies to realize an effective fault-tolerant routing. A novel fault-tolerant routing algorithm in hypercube multi-computers system is proposed, in which each node uses a maximum safety path matrices (MSPMs) to record the optimal paths to the other nodes. It proves that MSPMs can record most of the optimal paths by n-1 rounds of information exchanges between neighboring nodes. Furthermore, it proves that MSPMs is the final extension of the Optimal Path Matrices (OPMs) and the Extended Optimal Path Matrices (EOPMs) which also use the matrices to record the optimal paths in hypercube multi-computers system, so the problem of how to record the most of optimal paths in the n dimensional hypercube multi-computers system by using matrices is solved finally.