  We demonstrate novel features in the behavior of the second and third order
non-linearity parameters of the curvature perturbation, namely, $f_{NL}$ and
$g_{NL}$, arising from non-linear motion of curvaton field. We investigate two
classes of potentials for the curvaton - the first has tiny oscillations
super-imposed upon the quadratic potential. The second is characterized by a
single 'feature' separating two quadratic regimes with different mass scales.
The feature may either be a bump or a flattening of the potential. In the case
of the oscillatory potential we find that as the width and height of
superimposed oscillations increase, both $f_{NL}$ and $g_{NL}$ deviate strongly
from their expected values from a quadratic potential. $f_{NL}$ changes sign
from positive to negative as the oscillations in the potential become more
prominent. Hence, this model can be severely constrained by convincing evidence
from observations that $f_{NL}$ is positive. $g_{NL}$, on the other hand,
acquires very large negative values. For the the single feature potential, we
find that $f_{NL}$ and $g_{NL}$ exhibit oscillatory behavior as a function of
the parameter that controls the feature.
