Dubrovin and Ugaglia introduced a holomorphic Poisson structure on the space of semisimple Frobenius manifolds, which is identified with the entries of an upper triangular matrix with ones on the diagonal. In this talk, we compute explicitly the real forms of the Dubrovin-Ugaglia Poisson structures, arising from the real forms of the Lie algebra so(n,C). This is joint work with Zheheng Xiao and Xiaomeng Xu.