  In this paper we perform the analysis that leads to the space of initial
conditions for the Hamiltonian system $q' = p^2 + zq + \alpha$, $p' = -q^2 - zp
- \beta$, studied by the author in an earlier article. By compactifying the
phase space of the system from $\mathbb{C}^2$ to $\mathbb{CP}^2$ three base
points arise in the standard coordinate charts covering the complex projective
space. Each of these is removed by a sequence of three blow-ups, a construction
to regularise the system at these points. The resulting space, where the
exceptional curves introduced after the first and second blow-up are removed,
is the so-called Okamoto's space of initial conditions for this system which,
at every point, defines a regular initial value problem in some coordinate
chart of the space.
