  Doubling a Yang-Mills field we apply the pattern which has been found to
construct a "duality-symmetric" gravity with matter to the "duality-symmetric"
Yang - Mills theory in five space-time dimensions. Constructing the action we
conclude that dualizing a non-abelian theory requires non-locality. We analyze
the symmetries of the theory and equations of motion. Extension to the
supersymmetric theory is also demonstrated.
