We study the stable matching problem in which participants have complete and weak preference lists over the other participants. We focus on a new structure called the “super-stable partition” that characterizes the super-stability of the roommate problem under weak preferences. We show that a super-stable partition always exists and can be computed in polynomial time \(O(n^2)\) . The takeaway result is that a super-stable roommate matching exists if and only if the cardinality of each super ring in the super-stable partition is even.