  We investigate the curvaton dynamics and the non-linearity parameters in
curvaton model with potential slightly deviating from the quadratic form in
detail. The non-linearity parameter $g_{NL}$ will show up due to the curvaton
self-interaction. We also point out that the leading order of non-quadratic
term in the curvaton potential can be negative, for example in the axion-type
curvaton model. If a large positive $g_{NL}$ is detected, the axion-type
curvaton model will be preferred.
