Within the framework of the time-dependent local-density approximation (TDLDA) and the spherical background jellium model, we have estimated the photoionization cross sections for a medium-size closed-shell sodium cluster, Na20. We have also introduced a self-interaction correction to ensure the correct asymptotic behaviour of the potential seen by the ejected electron. Our results show that in contrast to the photoexcitation process, the photoionization cross sections are very sensitive to the approximation used to describe the cluster electrons. Futhermore, many-electron correlations are found to be very large. Similarly to the atomic case, when correct asymptotic conditions are taken properly into account, cross sections exhibit many one-electron autoionization resonances.