  In the context of modulated-symmetry distributions, there exist various forms
of skew-elliptical families. We present yet another one, but with an unusual
feature: the modulation factor of the baseline elliptical density is
represented by a distribution function with an argument which is not an odd
function, as it occurs instead with the overwhelming majority of similar
formulations, not only with other skew-elliptical families. The proposal is
obtained by going back to the use of Lemma~1 of Azzalini and Capitanio (1999),
which can be seen as the general frame for a vast number of existing
formulations, and use it on a different route. The broader target is to show
that this `mother lemma' can still generate novel progeny.
