The ${\germ{su}}(2)$ finite oscillator model introduced in N.~M. Atakishiev et al. [J. Phys. A {\bf 34} (2001), no.~44, 9381--9398; MR1875199 (2002k:81080)] is one of the most simple examples of a finite quantum system. Indeed, its physical operators (Hamiltonian, position, momentum) are elements of ${\germ{su}}(2)$ acting on a finite irreducible ${\germ{su}}(2)$ representation of dimension $2j+1$. The spectrum of position and momentum operators is the set $\{-j, -j+1, \dots, j-1,j\}$ and the corresponding discrete eigenfunctions are given in terms of Krawtchouk polynomials. The discrete Wigner function (a matrix) for the ${\germ{su}}(2)$ oscillator was computed for some particular values of $j$ in J. Van~der~Jeugt [J. Phys. A {\bf 46} (2013), no.~47, 475302; 3128860 ]. \par In the paper under review the authors give the explicit values of the entries of the Wigner matrix of the ${\germ{su}}(2)$ finite oscillator by using two approaches. The first one is based on hypergeometric series taking into account a basis transformation such that the Wigner matrix is obtained from a pre-Wigner matrix by a process involving Vandermonde matrices and their inverses. The second one has a combinatorial flavor. Indeed, the entries of the pre-Wigner matrix coincide with the Dyck polynomials, multivariable polynomials counting all Dyck paths of a certain type.