In this paper, we determine the index of the Clifford algebras of 6-dimensional quadratic forms over a field whose characteristic is unequal to 2. In the case that the characteristic is equal to 2, we compute the Clifford algebras of the Scharlau’s transfer of 4-dimensional quadratic forms with trivial Arf invariant, and then investigate how the index of the Clifford algebra of q depends on orthogonal decompositions of q when q is a low dimensional quadratic form.