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It is proved that a real-valued function $f\left(x\right)=exp\left(\pi i{\chi }_I\left(x\right)\right)$, where I is an interval contained in [0,1), is not of the form $f\left(x\right)=\overline{q\left(2x\right)}q\left(x\right)$ with |q(x)|=1 a.e. if I has dyadic endpoints. A relation of this result to the uniform distribution mod 2 is also shown.