  We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild
black hole. It proves out that the real parts of the complex quasinormal modes,
representing the real oscillation frequencies, are proportional to the product
of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The
asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived.
In addition the WKB formula for computing QN modes, developed to the 3rd order
beyond the eikonal approximation, is extended to the 6th order here. This gives
us an accurate and economic way to compute quasinormal frequencies.
