In this paper, let be a metacyclic 2-group of negative type of class two and ofclass at least three. Let O be the set of all subsets of all commuting elements of size two in the form of a,b, where a and b commute and |a|= |b|= 2.The probability that an element of a group fixes a set is considered as one of the extensions of the commutativity degree that can be obtained by some group actions on a set. In this paper, the probability that an element of fixes the set O under regular action is computed
