A general decomposition theory of ordered exponentials is presented by reducing the problem to the decomposition of ordinary exponential operators in terms of the super-operator _??_ defined by F(t)exp(Δt_??_)G(t)=F(t+Δt)G(t). It is proved that T(exp∫^t+Δt_tH(s)ds)=exp[Δt(H(t)+_??_)]. Here T denotes the time ordering.