In this paper we prove that if Φ is a modulus function and if X = [0,1] is given the Lebesgue measure, then M(LΦ) = LΦ, if and only if lim x – 0 Φ(x2)/ Φ(x) < ∞; LΦ being the Orlicz space LΦ (X); and M(LΦ) its multiplier algebra.