  We perform fits to the available charged and neutral kaon production data in
$e^++e^-\to K+X$, $K=K^\pm and K^0_S$, and determine the non-singlet
combination of kaon fragmentation functions $D_u^{K^\pm}-D_d^{K^\pm}$ in a
model independent way and without any correlations to the other fragmentation
functions. Only nuclear isospin invariance is assumed. Working with
non-singlets allows us to include the data at very low momentum fractions,
which have so far been excluded in global fits, and to perform a first NNLO fit
to fragmentation functions. We find that the kaon non-singlet fragmentation
function at large $z$ is larger than that obtained by the other collaborations
from global fit analysis and differs significantly at low $z$.
