Singular S-Hermitian systems are studied with the goal of defining a T
itchmarsh-Weyl M(lambda)-coefficient directly in terms of separated, s
elf-adjoint boundary conditions. A general deficiency index is allowed
. The resolvent operator is constructed and a self-adjoint operator A
is constructed in the Hilbert space which gives an equivalent descript
ion of the singular S-Hermitian boundary value problem.