  In this paper, we study the shape of the min-max minimal hypersurface
produced by Almgren-Pitts in \cite{A2}\cite{P} corresponding to the fundamental
class of a Riemannian manifold $(M^{n+1}, g)$ of positive Ricci curvature with
$2\leq n\leq 6$. We characterize the Morse index, area and multiplicity of this
min-max hypersurface. In particular, we show that the min-max hypersurface is
either orientable and of index one, or is a double cover of a non-orientable
minimal hypersurface with least area among all closed embedded minimal
hypersurfaces.
