  A complete flux-limited sample of 118 ultraluminous infrared galaxies (ULIGs)
has been identified from the IRAS Faint Source Catalog (FSC). The selection
criteria were a 60 micron flux density greater than 1 Jy in a region of the sky
delta > -40 deg, |b| > 30 deg. All sources were subsequently reprocessed using
coadded IRAS maps in order to obtain the best available flux estimates in all
four IRAS wavelength bands. The maximum observed infrared luminosity is L_ir =
10^{12.90} L_{sun}, and the maximum redshift is z = 0.268. The luminosity
function for ULIGs over the decade luminosity range L_ir = 10^{12} - 10^{13}
L_{sun} can be approximated by a power law Phi (L) ~= L^{-2.35} Mpc^{-3}
mag^{-1}. In the local Universe z < 0.1, the space density of ULIGs appears to
be comparable to or slightly larger than that of optically selected QSOs at
comparable bolometric luminosities. A maximum likelihood test suggests strong
evolution for our sample; assuming density evolution proportional to
(1+z)^{alpha} we find alpha = 7.6+/-3.2. Examination of the two-point
correlation function shows a barely significant level of clustering, xi (r) =
1.6 +/- 1.2, on size scales r ~= 22 h^{-1} Mpc.
