  We compute in this note the full homotopy type of the space of symplectic
embeddings of the standard ball $B^4(c) \subset \R^4$ (where $c= \pi r^2$ is
the capacity of the standard ball of radius $r$) into the 4-dimensional
rational symplectic manifold $M_{\mu}= (S^2 \times S^2, \mu \om_0 \oplus
\om_0)$ where $\om_0$ is the area form on the sphere with total area 1 and
$\mu$ belongs to the interval $(1,2]$. We know, by the work of
Lalonde-Pinsonnault, that this space retracts to the space of symplectic frames
of $M_{\mu}$ for any value of $c$ smaller than the critical value $\mu -1$, and
that its homotopy type does change when $c$ crosses that value. In this paper,
we compute the homotopy type for the case $c \ge \mu-1$ and prove that it is
not the type of a finite CW-complex.
