A graph \(G\) is said to be a circular arc graph if there exist circular arcs A\(g\), \(g\in V(G)\), such that \(g\), \(g'\) are adjacent in \(G\) if and only if the corresponding A\(g\), A\(_{g'}\) intersect. This paper shows that a graph with clique covering number two is a circular arc graph if and only if its edges can be coloured by two colours so that no induced four-cycle contains two opposite edges of the same colour.