  We report a new kind of exceptional points in periodically driven system,
called Floquet $\pi$ exceptional points, whose eigenvectors rotate on Bloch
sphere and accumulate $\pi$ geometric phase in one time period. The merging of
two such kind exceptional points are constrained by their dynamical structure,
meaning two order-1/2 exceptional points with same dynamical structure can
merge to one order-1 one while those with opposite dynamical structure can not.
We show they exist in Floquet bipartite lattices, and the order-1 Floquet $\pi$
exceptional points appear at the phase transition point between quasimomentum
gap phases and quasienergy gap phases. The scattering properties around the
order-1 Floquet $\pi$ exceptional points is quite novel, which is perfect
transparency but detectable in reflection for one of two sides.
