  In response to a well-known open question ``Does every complete geometric
graph on $2n\/$ vertices have a partition of its edge set into $n\/$ plane
spanning trees?" we provide an affirmative answer when the complete geometry
graph is in the regular wheel configuration. Also we present sufficient
conditions for the complete geometric graph on $2n\/$ vertices to have a
partition of its edge set into $n\/$ plane spanning trees (which are double
stars, caterpillars or $ w\/$-caterpillars).
