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