  For a class of singular Sturm-Liouville equations on the unit interval with
explicit singularity $a(a + 1)/x^2, a \in \mathbb{N}$, we consider an inverse
spectral problem. Our goal is the global parametrization of potentials by
spectral data noted by $\lambda^a$, and some norming constants noted by
$\kappa^a$. For $a = 0$ and $a=1$, $\lambda^a\times \kappa^a$ was already known
to be a global coordinate system on $\lr$. With the help of transformation
operators, we extend this result to any non-negative integer $a$ and give a
description of isospectral sets.
