Among various generalizations of continuity we can see two types; in one of them it is assumed that the inverse images of open sets belong to some class larger than the topology, this way leads - in particular - to quasi - continuous maps [11, 17]. In the second one the inverse images of sets from some subfamily of the given topology are considered. Then, as an example there are $s$-continuous maps [13, 14, 15]. Joinging both the above methods the class of s-quasi-continuous maps is introduced.