The authors define de following system in \(L^2([0,1])\): \[ \begin{aligned} d_0(x) = 1,\;d_j(x) &= \sum_{ l \mid \underline{j}} (-1)^{( l-1)/2} l^{-1} \mu( l) c_{j/ l}(x) \quad (j\geq1),\\ t_j(x) &= \sum_{ l \mid \underline{j}} l^{-1} \mu( l) s_{j/ l}(x) \quad (j\geq1), \end{aligned} \] where \(\mu\) is the Möbius function, \(\underline{j}\) is the quotient of \(j\) by its largest power-of-two factor, and \[ \begin{aligned} c_j(x) &= \text{ sgn}(\cos(2\pi jx)) = (-1)^{\lfloor 2jx+1/2\rfloor}\quad (j\geq0)\\ s_j(x) &= \text{ sgn}(\sin(2\pi jx)) = (-1)^{\lfloor 2jx\rfloor}\quad (j\geq1),\end{aligned} \] where \(\lfloor t\rfloor\) denotes the integer part of \(t\). The system contains the Rademacher functions, since \(r_ l(x)= s_{2^{ l-1}}(x)= t_{2^{ l-1}}(x) \), but it is different from the Walsh system. The functions of the system are shown to be pairwise orthogonal. Unfortunately, the proof of the completeness of the system is based on results proven in the paper (Corollaries 1 and 2) which are not correct (in particular, they imply that the Fourier series of any integrable function converges a.e.).