  We introduce semi-infinite Lakshmibai-Seshadri paths by using the
semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on
affine Weyl groups in place of the usual Bruhat order. These paths enable us to
give an explicit realization of the crystal basis of an extremal weight module
of an arbitrary level-zero dominant integral extremal weight over a quantum
affine algebra. This result can be thought of as a full generalization of our
previous result (which uses Littelmann's Lakshmibai-Seshadri paths), in which
the level-zero dominant integral weight is assumed to be a positive-integer
multiple of a level-zero fundamental weight.
