  The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three
dimensional space up to fourth-order in the first derivative is regarded as a
low-energy effective theory of SU(2) Yang-Mills theory. One can show from the
Wilsonian renormalization group argument that the effective action of
Yang-Mills theory recovers the SFN in the infrared region. However, the theory
contains another fourth-order term which destabilizes the soliton solution. In
this paper we derive an extended action including second derivative terms and
obtain soliton solutions numerically. A new topological lower bound formula is
infered for the extended action.
