An update of the first measurement of the Charm Structure Function of the Photon with reduced systematic and statistical uncertainties is presented. The inclusive production of charged D* mesons in deep inelastic electron-photon scattering has been used to extract the charm structure function of the photon in the kinematic range 0.0014 < x < 0.87 and 5 GeV^2 <Q^2 < 100 GeV^2. The data were taken with the OPAL detector at LEP at e+e- centre-of-mass energies from 183 to 209 GeV. The result is compared to a NLO perturbative QCD calculation.