  In this paper, we construct indecomposable integrally closed modules of
arbitrary rank over a two-dimensional regular local ring. The modules are quite
explicitly constructed from a given complete monomial ideal. We also give
structural and numerical results on integrally closed modules. These are used
in the proof of indecomposability of the modules. As a consequence, we have a
large class of indecomposable integrally closed modules of arbitrary rank whose
ideal is not necessarily simple. This extends the original result on the
existence of indecomposable integrally closed modules and strengthens the
non-triviality of the theory developed by Kodiyalam.
