  We study non-existence of non-constant regular maps from a partial flag
variety $X=G/P$ to another partial flag variety $X'=G'/P'$ and prove that there
does not exist any non-constant regular map from any partial non-complete flag
variety $X$ to any complete flag variety $X'=G'/B'$. We also formulate a
general conjecture on the non-existence of non-constant regular maps from $X\to
X'$.
