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In this paper, a new representation of the Wigner function for a quantumsystem in the phase space is proposed. The new representation is of the form$W=\operatorname{Sp}\left[ \rho \mathcal{W} \right]$, where $\rho$ is thedensity matrix, and $\mathcal{W}$ is the universal density matrix. The densitymatrix $\rho$ 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 theuniversal matrix $\mathcal{W}$ were found explicitly and their properties wereinvestigated. The diagonal elements of the matrix $\mathcal{W}$ are the Wignerfunctions of the harmonic oscillator, which do not introduce dissipation intothe quantum system. The off-diagonal elements of the matrix $\mathcal{W}$contain frequency oscillations responsible for dissipations in the quantumsystems.

Universal density matrix for the phase space