This paper is concerned with the proof of so-called Bramble-Hilbert Lemma. We present that Poincare`s inequality in [3] implies one of results of Morrey which is crucial in the proof. In this point of view, we recognize that removing the average term in Poincare`s inequality fulfills a crucial role in the proof of Bramble-Hilbert Lemma. It is accomplished by adding some polynomial of degree one less than the degree of the Sobolev space in the outset. So, the condition annihilating the set of polynomials Pk-1 of degree k-1 is required necessarily in Bramble-Hilbert Lemma.