The congruence lattices of algebras with a fixed finite base set A form a lattice ϵA (with respect to inclusion). The coatoms of EA are congruence lattices of monounary algebras (A, f), i.e., they are of the form Con(A, f) for a unary function f : A → A. It is known from [8] that there are three different types I, II, III of such coatoms which can be described explicitly by the corresponding type of f. In the present paper we are going to characterize these congruence lattices in detail. We prove that each coatom is a particular union of some nontrivial intervals of the partition lattice Eq(A). Moreover, for each monounary algebra (A, f) of type I, II, III the join- and meetirreducible elements, the atoms and the coatoms of its congruence lattice Con(A, f ) are determined, and the covering relation in this lattice is characterized.