  The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C
are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the
imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth
factor in Gaussian elimination is less than 3. In this paper, based on the
previous results, a new bound of the growth factor is obtained by using the
maximum of the condition numbers of matrixes B and C for the generalized Higham
matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.
