In this paper, we address a control design problem related to decoupling, namely robust decoupling. The idea of robust decoupling is defined and shown to be equivalent to robust performance of a Hadamard-weighted l(1) performance measure, A necessary and sufficient condition to determine if a compensator satisfies robust performance of a Hadamard-weighted l(1) performance measure in the presence of structured uncertainty is given, This condition can be used to determine if a compensator robustly decouples a plant. Finally, an iterative scheme for synthesizing a robust decoupling controller is discussed.