A new class of functions called ‘quasi perfectly continuous functions’ is introduced. Basic properties of quasi perfectly continuous functions are studied and their place in the hierarchy of variants of continuity, that already exist in the literature, is elaborated. The notion of quasi perfect continuity, in general is independent of continuity, but coincides with perfect continuity (Indian J. Pure Appl. Math. 15(3) (1984), 241-250), a sig-nificantly strong form of continuity, if the range space is regular.