  The well-known Schwarzschild black hole was first obtained as a stationary,
spherically symmetric solution of the Einstein's vacuum field equations. But
until thirty years later, efforts were made for the analytic extension from the
exterior area $(r>2GM)$ to the interior one $(r<2GM)$. As a contrast to its
maximally extension in the Kruskal coordinates, we provide a comoving
coordinate system from the view of the observers freely falling into the black
hole in the radial direction. We find an interesting fact that the spatial part
in this coordinate system is maximally symmetric $(E_3)$, i.e., along the world
lines of these observers, the Schwarzschild black hole can be decomposed into a
family of maximally symmetric subspaces.
