In this paper, we classify all n-dimensional generalized Heisenberg Lie algebras of rank (n – 4), and to this end, we demonstrate that for any n-dimensional generalized Heisenberg Lie algebra, if the rank is (n – 4), then such an algebra does not exist when n ⩾ 11. We also show that for a n-dimensional 2-step nilpotent Lie algebra L with the derived subalgebra of dimension r, we have r ⩽ n + [1-√8n+1/2].