Knowledge of the Earth's changing rotation is fundamental to positioning objects in space and on the planet. Nowadays, the Earth's orientation in space is expressed by five Earth Orientation Parameters (EOP). Many applications in astronomy, geosciences, and space missions require accurate EOP predictions. Operational predictions are released daily by the Rapid Service/Prediction Centre of the International Earth Rotation and Reference Systems Service (IERS). The prediction procedures and performances differ for the three EOP classes: polar motion, rotation angle (UT1-UTC), and the two celestial pole offsets (CPO), dX and dY. The IERS Annual Report 2016 shows Rapid Service CPO predictions errors with respect to IERS 08 C04 observations in 2016 ranging from 120 to 140 μas in 40 days for dX, and 100-160 μas for dY. We test a new method for the CPO prediction based on the recent availability of sophisticated empirical models for the Free Core Nutation, a main component of the CPO variations. We found it allows predicting both CPO with error estimates for the period 2000-2016 lower than the 2016 Rapid Service products, reaching about 85 μas after 40 days and near 90 μas after a year. These results would represent a 35-40% improvement.