  The subtraction method for the matching between the matrix element (ME) and
parton shower (PS), that has been developed for combining 0-jet and 1-jet
production processes in association with electroweak-boson production in hadron
collisions, is extended to multi-jet production. In order to include multi-jet
MEs, we have to address the soft-gluon divergence together with the collinear
divergence. We introduce an approximation which simultaneously reproduces both
divergences in a form suitable for application to our subtraction method. The
alteration in the subtraction can be compensated by applying an appropriate
correction to corresponding non-radiative events. We demonstrate that $W$ + 0,
1, and 2 jet production processes can be consistently combined using the
developed matching method.
