Once it has exhausted all possible fuel, a large star will end its life as a core-collapse supernova. Although the emitted light briefly outshines an entire galaxy, 99% of the energy from such a supernova is released as neutrinos. A burst of these supernova neutrinos was seen twenty-four years ago, from the star Sanduleak -69 202a, in an event known as Supernova 1987a. Whilst the next such burst is eagerly anticipated, it is also possible to detect the supernova relic neutrino background, comprised of neutrinos from all past core-collapse supernovae. One such search was conducted using 1496 days of data from the Super-Kamiokande detector. This analysis looked for electron-type anti-neutrinos that had produced a positron with an energy greater than 18 MeV. In the absence of a signal, 90% C.L. upper limits on the total flux were set for several theoretical models; these limits ranged from 20 to 130 nu_e bar cm^-2 s^-1. Additionally, an upper bound of 1.2 nu_e bar cm^-2 s^-1 was set for the supernova relic neutrino flux in the energy region E_nu > 19.3 MeV.