Abstract: Let η ( z ) be Dedekind’s η -function. For any set of integer g = ( k 1 …, K s ), k 1 ≥ k 2 ≥ … ≥ k s ≥ 1, put . In this paper, we shall prove McKay’s conjecture which gives some combinatorial conditions about k i on which η g ( z ) is a primitive cusp form. As to McKay’s conjecture, we refer [5].