  Motivated by bouncing motion of an inelastic particle on a vibrating board, a
simple two-dimensional map is constructed and its behavior is studied
numerically. In addition to the typical route to chaos through a periodic
doubling bifurcation, we found peculiar behavior in the parameter region where
two stable periodic attractors coexist. A typical orbit in the region goes
through chaotic motion for an extended transient period before it converges
into one of the two periodic attractors. The basin structure in this parameter
region is almost riddling and the fractal dimension of the basin boundary is
close to two, {\it i.e.}, the dimension of the phase space.
