We report on a search for new particles in the diphoton channel using a data sample of pp collisions at s√=1.96  TeV collected by the CDF II detector at the Fermilab Tevatron, with an integrated luminosity of 5.4  fb−1. The diphoton invariant mass spectrum of the data agrees well with the standard model expectation. We set upper limits on the production cross section times branching ratio for the Randall-Sundrum graviton, as a function of diphoton mass. We subsequently derive lower limits on the graviton mass of 459  GeV/c2 and 963  GeV/c2, at the 95% confidence level, for coupling parameters (k/MPl) of 0.01 and 0.1, respectively.