8 periments, the properties and decays of the massive me- diators of the electroweak interaction, the W and Z vec- tor bosons, have been studied extensively. The exclu- sive leptonic final states of the boson decays, Z → l $^{+}$l − and W ± → l $^{±}$ν , have been observed and are well- understood. Hadronic decays of the bosons have also been observed, but no exclusive final states predicted by the standard model (SM) have been identified. A class of these unobserved vector boson decay channels, radia- tive decays ( V → P + γ ), where P is a pseudoscalar meson, are sensitive probes of the strong dynamics in- volved in meson formation as well as of the vector bo- son couplings to the photon. These radiative decays are rare because their branching ratios are suppressed by a factor of ( f$_{P}$ /M$_{W,Z}$ ) $^{2}$, where f$_{P}$ is the meson form fac- tor. Standard model predictions for the branching ratio of the decay of the W boson to charged pion and pho- ton ( W ± → π $^{±}$γ ) range from ∼ 10 − 6 to ∼ 10 − 8 [3]. However, the sensitivity of the Tevatron experiments to observing these rare decays, especially W ± → π $^{±}$γ , is ap- proaching the upper range of the SM predictions. Mea- surement of the cross section of these radiative W and Z boson decays would provide information about these poorly understood SM processes, especially involving me- son form factors at high energies. Previous searches for the W ± → π $^{±}$γ de- cay by the UA1, UA2, and CDF experiments have successively brought the upper limit on Γ( W ± → π $^{±}$γ ) / Γ( W ± → e $^{±}$ν ) down to the level of 7 × 10 − 4 at 95% confidence level (C.L.)[4, 5]. 9PL, England, $^{q}$Queen Mary, University of London, London, E1 4NS, England, $^{r}$University of Melbourne, Victoria 3010, Australia, $^{s}$Muons, Inc., Batavia, IL 60510, $^{t}$Nagasaki Institute of Applied Science, Nagasaki, Japan, $^{u}$National Research Nuclear University, Moscow, Russia, $^{v}$University of Notre Dame, Notre Dame, IN 46556, $^{w}$Universidad de Oviedo, E-33007 Oviedo, Spain, $^{x}$Texas Tech University, Lubbock, TX 79609, $^{y}$Universidad Tecnica Fed- erico Santa Maria, 110v Valparaiso, Chile, $^{z}$Yarmouk University, Irbid 211-63, Jordan, $^{hh}$On leave from J. Stefan Institute, Ljubl- jana, Slovenia, In this Letter we present a search for the W ± → π $^{±}$γ decay using data corresponding to 4 . 3 fb − 1 of integrated luminosity recorded by the CDF experiment in p ¯ p colli- sions at 1.96 TeV. Compared to the previous CDF search [5], this represents an increase in the size of the data set