  For the class of central potentials possessing a finite number of bound
states and for which the second derivative of $r V(r)$ is negative, we prove,
using the supersymmetric quantum mechanics formalism, that an increase of the
angular momentum $\ell$ by one unit yields a decrease of the number of bound
states of at least one unit: $N_{\ell+1}\le N_{\ell}-1$. This property is used
to obtain, for this class of potential, an upper limit on the total number of
bound states which significantly improves previously known results.
