In this talk.we report for a measurement of the high-order scaling exponents ξF(q)[(forward) and ξI(q) (inverse) of a dual-cascade of the vorticity in two-dimensional (2D) turbulence.This is accomplished by applying a Hilbert-based tcchnique to the vorticity fields obtained from a high-resolution direct numerical simulation of the 2D rurbulcnce with an Ekman friction.It confirms that the inverse enstrophy cascade is nonintermittent with a scaling exponent linear with the statistical order q.In the inverse cascade.the vorticity probability density function (pdf) p(k, ω) has an exponential tail for all wavenumber k.In the forward enstrophy cascade, the pdf core kernel is changing asymptotically from Gaussian to the exponential one.The expcrimcntal cascade scaling exponent ξωF(q) of vorticity arc nonlinear and can be described by a log-Poison formula very well.We thus characterize the intermittent property of the vorticity in the 2D turbulence directly without applying the ExtendedSelf-Similarity technique.