A natural and geometrical definition of projective space $(P_n(\Bbb B),g_0)$, based on the algebra of paraquaternionic numbers $\Bbb B$, is given. Using the technique of pseudo-Riemannian submersions, we determine the curvature of the paraquaternionic space $(P_n(\Bbb B),g_0)$. Moreover, the properties of this curvatures are studied.