  In this paper, we will use $\delta \mathcal{N}$-formalism to calculate the
primordial curvature perturbation for the curvaton model with a Lagrange
multiplier field. We calculate the non-linearity parameters $f_{NL}$ and
$g_{NL}$ in the sudden-decay approximation in this kind of model, and we find
that one could get a large non-Gaussinity even if the curvaton dominates the
total energy density before it decays, and this property will make the curvaton
model much richer. We also calculate the probability density function of the
primordial curvature perturbation in the sudden-decay approximation, as well as
some moments of it.
