  In this paper, we discuss a property of the Kullback--Leibler divergence
measured between two models of the family of the location-scale distributions.
We show that, if model $M_1$ and model $M_2$ are represented by location-scale
distributions, then the minimum Kullback--Leibler divergence from $M_1$ to
$M_2$, with respect to the parameters of $M_2$, is independent from the value
of the parameters of $M_1$. Furthermore, we show that the property holds for
models that can be transformed into location-scale distributions. We illustrate
a possible application of the property in objective Bayesian model selection.
