  We compute the homology of the complexes of finite Verma modules over the
annihilation superalgebra $\mathcal A(K'_{4})$, associated with the conformal
superalgebra $K'_{4}$, obtained in \cite{K4}. We use the computation of the
homology in order to provide an explicit realization of all the irreducible
quotients of finite Verma modules over $\mathcal A(K'_{4})$.
