In this paper coefficients $A(s) \in c^\infty [0,1]$, $B(s) \in c^\infty [0,1]$ are constructed so that given positive numbers $\lambda _1 < \lambda _2 < \cdots < \lambda _n $, are the first n eigenvalues and given positive numbers $\rho _1 , \cdots ,\rho _n $ are the first n normalization constants for the first n eigenfunctions for the fourth order self-adjoint eigenvalue problem $y^{(4)} + (Ay^{(1)} )^{(1)} + By - \lambda y = 0$, $y(0) = y^{(1)} (0) = y(1) = y^{(1)} (1) = 0$. The solution is determined from the spectral function for the eigenvalue problem.