In this paper, we will provide an alternative proof to characterize the pointwise multipliers which maps a Sobolev space Ḣr (ℝd) to its dual Ḣr (ℝd) in the case 0 < r < d2 by a simple application of the definition of fractional Sobolev space. The proof relies on a method introduced by Maz'ya-Verbitsky [9] to prove the same result. © 2013 The Korean Mathematical Society.