Using our proof of the Poincare conjecture in dimension three and the method of mathematical induction a short and transparent proof of the generalized Poincare conjecture (the main theorem below) has been obtained. Main Theorem. Let Mⁿ be a n-dimensional, connected, simply connected, compact, closed, smooth manifold and there exists a smooth finite triangulation on Mⁿ which is coordinated with the smoothness structure of Mⁿ. If Sⁿ is the n-dimensional sphere then the manifolds Mⁿ and Sⁿ are homemorphic.