  Necessary and sufficient conditions for two sequences
$\{\mu_n\}_{n=0}^\infty$ and $\{ a_n\}_{n=0}^\infty$ to be the spectral data
for a certain Sturm-Liouville problem are well known. We add two more
conditions so that the same two sequences become necessary and sufficient for
being the spectral data for a Sturm-Liouville problem with fixed boundary
conditions.
