In　this　paper,　the　semigroup　Hn(L)　of　Hall　matrices　over　a　complete　and　completely　distributive　lattice　L　is　studied.　A　Hall　matrix　is　a　matrix　which　is　greater　(for　the　order　associated　with　the　lattice　structure)　than　an　invertible　matrix.　Some　necessary　and　sufficient　conditions　for　a　Hall　matrix　to　be　regular　in　the　semigroup　Hn(L)　are　given　and　Green＇s　relations　of　the　semigroup　Hn(L)　are　described.　Also,　the　sandwich　semigroup　of　Hall　matrices　over　the　lattice　L　is　studied.