The Walsh-Paley system \(\{w_n\}^\infty_{n= 0}\) on the unit interval \([0, 1]\) is defined using Rademacher functions \(r_k\), where \(r_k(x)\) is 1 or \(-1 \) depending on whether \(x\) belongs to an even or odd dyadic interval of \(k\)th level, and \(w_n(x)= \prod r_k(x)^{n_k}\) for \(n= \sum n_k 2^k\) \((n_k= 0, 1)\). In the reviewed article the author introduces an orthogonal system of functions on the unit disc (polar Walsh system). It is defined analogously as Walsh-Paley system using polar Rademacher functions \(\phi_k\) (\(\phi_k\) rose up from a partition of the unit disk into \(2^k\) parts). The construction ensures the existence of a measure-preserving transformation of the unit disc onto \([0, 1]\) which is one-to-one off some set of measure zero and transforms one orthonormal system onto another one. Moreover, because of the similarity between the partitions of the interval \([0, 1]\) into dyadic intervals and the partitions of the unit disc, Walsh-Paley techniques work also in the polar setting and the results concerning to completeness, convergence properties of Fourier series, and uniqueness of the expansion, which are valid for the Walsh-Paley system, hold true also in the polar case. This shows that the introduced system has much better convergence and uniqueness properties than the double Walsh-Paley system on the unit square.