By using the notion of decreasing scale in the sense of \textit{D.C.J. Burgess} and \textit{M. Fitzpatrick} [Math. Proc. Camb. Phil. Soc. 82, 59--65 (1977; Zbl 0364.54026)], a theorem is proved on the existence of a pair \((U,V)\) of continuous real-valued functions from a topological space \(X\) representing an interval order \(\prec\) on \(X\) (for all \(x,y\in X\), \(x\prec y\) if and only if \(U(x)\leq V(y)\)).