In　order　to　correct　errors　in　a　previously　published　work　on　a　treatment　of　two-dimensional　coupled-wave　theory,　a　complete　derivation　of　the　two-dimensional　`overlap　grating＇　coupled　wave　equations　is　given.　By　using　the　Riemann　method,　a　corrected　solution　to　the　equations　in　closed　mathematical　form　is　obtained.　On　the　basis　of　this　solution　a　brief　investigation　of　the　diffraction　properties　of　finite-sized　gratings,　and　in　particular　the　dependence　of　diffraction　efficiency　on　the　geometric　size　of　gratings,　is　given.