Let \(K=\mathbb{Q}(\sqrt{p},\sqrt{d})\) be a real biquadratic field with p≡1 mod 4 or p=2, and d a squarefree positive integer. The Hilbert genus field is described explicitly by Yue (Ramanujan J. 21:17–25, 2010) in the case that p≡1 mod 4 and d≡3 mod 4. In this article, we give the Hilbert genus field of K explicitly for the remaining cases. We also consider the function field analogue of this problem.