  We present some new results on the rational solutions of the
Knizhnik-Zamolodchikov equation for the four-point conformal blocks of isospin
I primary fields in the SU(2)_k Wess-Zumino-Novikov-Witten model. The rational
solutions corresponding to integrable representations of the affine algebra
su(2)_k have been classified by Michel, Stanev and Todorov; provided that the
conformal dimension is an integer, they are in one-to-one correspondence with
the local extensions of the chiral algebra. Here we give another description of
these solutions as specific braid-invariant combinations of the so called
regular basis and display a new series of rational solutions for isospins I =
k+1 corresponding to non-integrable representations of the affine algebra.
