We have identified a total of 1272 newly recognized emission regions in M33. Combined with the previously cataloged total of 1066 H II regions and supernova remnants, this brings M33's total to 2338 emission regions. This paper provides photometry of the new objects in H{alpha}, which is combined with data from previous catalogs to produce a global H II region luminosity function (corrected for incompleteness) that reaches a faint luminosity limit of 2x10^34^ergs/s and shows a broad maximum with a peak frequency at luminosities of 6x10^35^ergs/s. We also plot the H II region size distribution and comment on unusual morphologies.