  Relative entropy is an essential tool in quantum information theory. There
are so many problems which are related to relative entropy. In this article,
the optimal values which are defined by $\displaystyle\max_{U\in{U(\cX_{d})}}
S(U\rho{U^{\ast}}\parallel\sigma)$ and $\displaystyle\min_{U\in{U(\cX_{d})}}
S(U\rho{U^{\ast}}\parallel\sigma)$ for two positive definite operators
$\rho,\sigma\in{\textmd{Pd}(\cX)}$ are obtained. And the set of
$S(U\rho{U^{\ast}}\parallel\sigma)$ for every unitary operator $U$ is full of
the interval $[\displaystyle\min_{U\in{U(\cX_{d})}}
S(U\rho{U^{\ast}}\parallel\sigma),\displaystyle\max_{U\in{U(\cX_{d})}}
S(U\rho{U^{\ast}}\parallel\sigma)]$
