We study the indexed Hermitean lattice of type 0 generated by a single element a subjected to the relation a ≤ b⊥ ∧ bb⊥= 0. We prove that it is finite, provided that two crucial indices are finite. We show that index relations imply algebraic relations and describe the lattice by means of its subdirectly irreducible factors. We finally use the results to confirm a conjecture appeared in 2000.