We calculate the Ohtsuki invariants λ i (M) (i = 0 , 1 , 2 , 3) of every Brieskorn–Hamm manifold M which is a rational homology 3 -sphere. We denote the order of H 1 (M ; ℤ) by H. By the result, we show that the third Ohtsuki invariant λ 3 (M) of the Brieskorn–Hamm manifolds M with H = 1 is negative, and the third Ohtsuki invariant λ 3 (M) of most Brieskorn–Hamm manifolds M with H ≥ 2 is positive.