A non explicit counterexample to a problem of quasi-normality

Here we give, in the case k=2, a counterexample to show that if the condition on the multiplicities of the zeros is omitted, then the local uniform boundedness of F2 does not even imply quasi-normality. In addition, we give a simpler proof for the Li-Xie theorem (and an extension of it) that does not use Nevanlinna's Theory which was used in the original proof.