Segments on a plane: problem

There are n white points and n black points on a plane. All are distinct and no three are on the same line. You must draw n segments, each between points of different colors. Segments must not intersect. (This also means they can't have a common endpoint.) Show that it's always possible to complete the task.

Send solutions to radugrigore at gmail. I'll post the list of solvers and a solution in a week. Please use the comments only to ask for clarifications, not to give the solution.