We consider a universal relation between moment of inertia and quadrupole moment of arbitrarily fast rotating neutron stars. Recent studies suggest that this relation breaks down for fast rotation. We find that it is still universal among various sug
gested equations of state for constant values of certain dimensionless parameters characterizing the magnitude of rotation. One of these parameters includes the neutron star radius, leading to a new universal relation expressing the radius through the mass, frequency, and spin parameter. This can become a powerful tool for radius measurements.
