Function in VMO$(S^1,S^1)$

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I try to find a function $f:S^1\rightarrow S^1$ that is in VMO but not continous. Does someone have a clue? VMO: http://www.ams.org/journals/tran/1975-207-00/S0002-9947-1975-0377518-3/S0002-9947-1975-0377518-3.pdf

Yours, Maxi