  The usual action of Yang-Mills theory is given by the quadratic form of
curvatures of a principal G bundle defined on four dimensional manifolds. The
non-linear generalization which is known as the Born-Infeld action has been
given. In this paper we give another non-linear generalization on four
dimensional manifolds and call it a universal Yang-Mills action. The advantage
of our model is that the action splits {\bf automatically} into two parts
consisting of self-dual and anti-self-dual directions. Namely, we have
automatically the self-dual and anti-self-dual equations without solving the
equations of motion as in a usual case. Our method may be applicable to recent
non-commutative Yang-Mills theories studied widely.
