  Let $M_{d}(\P^r)$ be the space of $(r+1)$-tuples $(f_0,...,f_r)$ modulo
homothety, where $f_0,...,f_r$ are homogeneous polynomials of degree $d$ in two
variables. Let $M_{d}^{\circ}(\P^r)$ be the open subset of $M_{d}(\P^r)$ such
that $f_0,...,f_r$ have no common zeros. Then $M_{d}^{\circ}(\P^r)$
parametrizes the space of holomorphic maps of degree $d$ from $\P^1$ into
$\P^r$. In general the boundary divisor $M_{d}(\P^r) \setminus
M_{d}^{\circ}(\P^r)$ is not normal crossing. In this paper we will give a
natural stratification of this boundary and show that we can process an
iterated blow-ups along these strata (or its proper transformations) to obtain
a compactification of $M_{d}^{\circ}(\P^n)$ with normal crossing divisors.
