We report on a new measurement of the branching ratio B(KL->pi0 gamma gamma)using the KTeV detector. We reconstruct 1982 events with an estimated background of 608, that results in B(KL -> pi0 gamma gamma) = (1.29 +/- 0.03(stat) +/- 0.05(syst)) x 10**-6. We also measure the parameter, aV, which characterizes the strength of vector meson exchange terms in this decay. We find aV = -0.31 +/- 0.05(stat) +/- 0.07(syst). These results utilize the full KTeV data set collected from 1997 to 2000 and supersede earlier KTeV measurements of the branching ratio and aV.