Let K = Q(root p, root d) be a real biquadratic field with p equivalent to 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 equivalent to 1 mod 4 and d equivalent to 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.