For a nilpotent Lie algebra L of dimension n and dim (L ²) = m ≥ 1, we find the upper bound , where M(L) denotes the Schur multiplier of L. In case m = 1, the equality holds if and only if L ≅ H(1) ⊕ A, where A is an abelian Lie algebra of dimension n − 3 and H(1) is the Heisenberg algebra of dimension