  Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a generalized flag manifold,
where $G$ is a real noncompact semi-simple Lie group and $P_{\Theta }$ a
parabolic subgroup. A classical result says the Schubert cells, which are the
closure of the Bruhat cells, endow $\mathbb{F}_{\Theta}$ with a cellular CW
structure. In this paper we exhibit explicit parametrizations of the Schubert
cells by closed balls (cubes) in $\mathbb{R}^{n}$ and use them to compute the
boundary operator $\partial $ for the cellular homology. We recover the result
obtained by Kocherlakota [1995], in the setting of Morse Homology, that the
coefficients of $\partial $ are $0$ or $\pm 2$ (so that
$\mathbb{Z}_{2}$-homology is freely generated by the cells). In particular, the
formula given here is more refined in the sense that the ambiguity of signals
in the Morse-Witten complex is solved.
