We adopt a non-oscillatory central scheme, first presented in the context of Hyperbolic conservation laws in [nessyahu-tadmor] followed by [jiang-tadmor], to the framework of the incompressible Euler equations in their vorticity formulation. The embedded duality in these equations, enables us to toggle between their two equivalent representations - the conservative Hyperbolic-like form vs. the convective form. We are therefore able to apply local methods, to problems with a global nature. This results in a new stable and convergent method which enjoys high-resolution without the formation of spurious oscillations. These desirable properties are clearly visible in the numerical simulations we present.