It is shown that if \(t > 1\) and \(u \geq 5\), then the known necessary condition for the existence of a skew Room frame of type \(t^u\), is also sufficient with the possible exception of \((u, f)\) where \(u = 5\) and \(t \in \{11, 13, 17, 19, 23, 29, 31, 41, 43\}\).