  We propose a novel first-order formalism for a type of $K$-brane systems. An
example solution is presented and studied. We illustrate how the noncanonical
kinetic term can affect the properties of the model, such as the stability of
the solutions, the localization of fermion and graviton. We argue that our
solution is stable against linear perturbations. The tensor zero mode of
graviton can be localized while the scalar zero mode cannot. The localization
condition for fermion is also discussed.
