A problem still unsolved in cosmology is the identification of the sources of radiation able to reionize H i in the intergalactic medium (IGM) by zsimilar to 6. Theoretical work and observations seem to indicate that the fraction, <f (esc) >, of H i ionizing radiation emitted from galaxies that escapes into the IGM is small in the local Universe (<f(esc)>less than or similar to 10 per cent). At high redshift, galaxies are more compact and probably gas-rich, implying smaller values of <f (esc)> from their discs or spheroids. However, if the sites of star formation are displaced from the disc or spheroid and the star formation efficiency of the proto-clusters is high, then <f (esc)> should be about 1. This star formation scenario is consistent with several models for globular cluster formation. Using simple arguments based on the observed number of globular cluster systems in the local Universe, and assuming that the oldest globular clusters formed before reionization and had <f(esc)>similar to1, I show that they produced enough ionizing photons to reionize the IGM at zapproximate to 6.