  We give a path model for a level zero extremal weight module over a quantum
affine algebra. By using this result, we prove a branching rule for an extremal
weight module with respect to a Levi subalgebra. Furthermore, we also show a
decomposition rule of Littelmann type for the concatenation of path models for
an integrable highest weight module and a level zero extremal weight module in
the case where the extremal weight is minuscule.
