  In this paper, a new representation of the Wigner function for a quantum
system in the phase space is proposed. The new representation is of the form
$W=\operatorname{Sp}\left[ \rho \mathcal{W} \right]$, where $\rho$ is the
density matrix, and $\mathcal{W}$ is the universal density matrix. The density
matrix $\rho$ for each quantum system is different, and the universal matrix
$\mathcal{W}$ is the same for any quantum system. Thus, the matrix
$\mathcal{W}$ has a fundamental character. In the work, the elements of the
universal matrix $\mathcal{W}$ were found explicitly and their properties were
investigated. The diagonal elements of the matrix $\mathcal{W}$ are the Wigner
functions of the harmonic oscillator, which do not introduce dissipation into
the quantum system. The off-diagonal elements of the matrix $\mathcal{W}$
contain frequency oscillations responsible for dissipations in the quantum
systems.
