In this letter, we report the competing growth of a Pd shell on the {110} and {100} facets of Au nanorods (Au NRs). This results in the disappearance of unstable {110} facets and the formation of rectangularly shaped Pd/Au bimetallic nanorods that show only four stable {100} side surfaces. The energy minimization to a more stable morphology is believed to be the driving force for the formation of the rectangular shape of the Pd shell.