  We introduce a class of states so-called semi-SSPPT (semi super strong
positive partial transposition) states in infinite-dimensional bipartite
systems by the Cholesky decomposition in terms of operator matrices and show
that every semi-SSPPT state is separable. This gives a method of constructing
separable states and generalizes the corresponding results in [Phys. Rev. A
\textbf{77}, 022113(2008), J. Phys. A: Math. Theor. 45 505303 (2012)]. This
criterion is specially convenient to be applied when one of the subsystem is a
qubit system.
