Divergent Fourier series with respect to orthonormalized systems of smooth functions

In this paper it is proved that for any function $f\in L^2[-\pi;\pi]$, $\|f\|_2>0$, there exists a complete orthonormalized system of uniformly bounded trigonometric polynomials with respect to which the Fourier series of this function is divergent almost everywhere in the interval $[-\pi;\pi]$.