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 sup
ernova remnants, this brings M33's total to 2338 emission regions. This pap
er provides photometry of the new objects in H alpha, which is combined wit
h data from previous catalogs to produce a global H II region luminosity fu
nction (corrected for incompleteness) that reaches a faint luminosity limit
of 2 x 10(34) ergs s(-1) and shows a broad maximum with a peak frequency a
t luminosities of 6 x 10(35) ergs s(-1). We also plot the H II region size
distribution and comment on unusual morphologies.