A function \(f\) is said to be a strong Świątkowski function if whenever \(\alpha , \beta \in I\) and \( y \in I(f(\alpha),f(\beta))\), there is an \(x_0 \in I(\alpha,\beta) \cap C(f)\) such that \(f(x_0) = y\) where \(I\) is a nondegenerate interval, \(I(a,b) = (a,b)\) if \(a < b\) and \((b,a)\) otherwise and \(C(f)\) denotes the set of all points of continuity of \(f\). One can easily see that strong Świątkowski functions are both Darbaux and quasi-continuous. Till now some research have been done to investigate which functions can or cannot be written as the product of a finite number of such functions and when it can be written what is the number of such functions in the product. For example, the sign function can be written as the product of three strong Świątkowski functions but it cannot be written as the product of two such functions. In an earlier paper the author has already shown that there is a function which can be written as the product of four such functions but cannot be written as the product of three. In this paper, he continues this investigation and finds a characterisation of the product of four or more strong Świątkowski functions. In his main result he proves that a function \(f\) is the product of four or more such functions if and only if the function \(f\) is cliquish, the set \([f = 0] = \{x \in I : f(x) =0\}\) is simply open, and there is a \(G_\delta\)-set \(A \subset [f = 0]\) such that for all \(a,b \in R\), if \(f(a)f(b) <0\), then \(A \cap I(a,b) \neq \emptyset\). The author also proves several interesting lemmas which are finally used to prove the main result.