We present a family of high-order, essentially non-oscillatory,
central schemes for
approximating solutions of hyperbolic systems of conservation laws.
These schemes are based on a new centered version of the Weighed
Essentially Non-Oscillatory (WENO) reconstruction of point-values
from cell-averages, which is then followed by an accurate approximation
of the fluxes via a natural continuous extension of Runge-Kutta solvers.
We explicitly construct the third and fourth-order scheme and demonstrate their
high-resolution properties in several numerical tests.