In this paper we introduce a new notion of m-quasi irresolute functions as functions from a set satisfying some minimal conditions into a topological space. We obtain some characterizations and several properties of such functions. This function lead us to the formulation of a unified theory of $(\theta, s)$-continuity [26], $\alpha$-quasi irresolute [24], weakly $\theta$-irresolute [19], $\theta$-irresolute [27], $\beta$-quasi irresolute [23].