  In this paper we try to further explore the linear model of the moduli of
rational maps. Our attempt yields following results. Let $X\subset \mathbf P^n$
be a generic hypersurface of degree $h$. Let $R_d(X, h)$ denote the open set of
the Hilbert scheme parameterizing irreducible rational curves of degree $d$ on
$X$. We obtain that (1) If $4\leq h\leq n-1$, $R_d(X, h)$ is an integral, local
complete intersection of dimension \begin{equation} (n+1-h)d+n-4.
\end{equation}
  (2) If furthermore $(h^2-n)d+h\leq 0$ and $h\geq 4$, in addition to part (1),
$R_d(X, h)$ is also rationally connected.
