An extension of the Parker bound on the flux F of magnetic monopoles l
eads to a stronger bound than obtained previously. The survival and gr
owth of a small galactic seed field requires F less-than-or-equal-to 1
0(-16)(m/10(17) GeV) cm-2 s-1 sr-1. This new limit rules out the possi
bility that monopoles much lighter than 10(17) GeV/c2 can provide the
closure density of the Universe.