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It is well--known that certain properties of continuous functions on thecircle $\mathbb T$, related to the Fourier expansion, can be improved by achange of variable, i.e., by a homeomorphism of the circle onto itself. One ofthe results in this area is the Jurkat--Waterman theorem on conjugatefunctions, which improves the classical Bohr--P\'al theorem. In the presentwork we provide a short and technically very simple proof of theJurkat--Waterman theorem. Our approach yields a stronger result.

A short and simple proof of the Jurkat--Waterman theorem on conjugate functions