Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. This paper focuses on systems that are both self-stabilizing and Byzantine tolerant. Combining these two properties is known to induce many impossibility results. Hence, there exist several fault tolerance schemes to contain Byzantine faults in self-stabilization. In this paper, we consider the well known problem of constructing a maximum metric tree in this context. We provide a new distributed protocol that ensures the best possible containment with respect to topology-aware strict and strong stabilization.