  In this paper, we give an atomic decomposition characterization of flag Hardy
spaces $H^p_F({\rr}^n\times {\rr}^m)$ for $0<p\le 1$, which were introduced in
\cite{hl1}. A remarkable feature of atoms of such flag Hardy spaces is that
these atoms have only partial cancellation conditions. As an application, we
prove a boundedness criterion for operators on flag Hardy spaces.
