Let R and B be two disjoint sets of points in the plane such that |B| ≤ |R|, and no three points of R⋃B are collinear.We show that the geometric complete bipartite graph K(R,B) contains a non-crossing spanning tree whose maximum degree is at most max [Formula presented]; this is the best possible upper bound on the maximum degree.This solves an open problem posed by Abellanas et al.at the Graph Drawing Symposium, 1996.