  In this paper, we give an explicit criterion when a rational holomorphic map
between balls is equivalent to a polynomial holomorphic map. Making use of this
criterion, we show that any proper rational holomorphic map from B^2 into B^N
of degree two is equivalent to a polynomial holomorphic map; we also construct
rational holomorphic maps of degree 3 that are almost linear but are not
equivalent to polynomial holomorphic maps.
