The space of negative power series of $z$ on $\{z\in \mathbb{C}:|z|>1\}$ can also be parametrized by means of a system of double bracket differential equations. To show this parametrization we introduce a group factorization for equation system. This work, for the case of a double bracket system, is a continuation of an earlier study discussed in The discrete KP hierarchy and the negative power series on the complex plane. Comp. and App. Math. 32 (2013), 483-493 for the case of one bracket system.